Theorem of the Day
The main purpose of this bibliography is to collect all the books given as "Further Reading" on individual theorem pages. Numbers in square brackets against an entry link to the theorems which cite it.
Clicking on the book names will take you to amazon.co.uk where you will find more detailed bibliographic information, customer reviews and, increasingly, their excellent 'Search Inside' facility.
If you buy the book during your visit to amazon.co.uk I receive a referral fee, for which I am grateful. However, inclusion of a book in this bibliography does not mean the book is recommended. Wherever possible an expert review is cited, denoted by the word Review, and these are by no means always entirely complimentary!
Reviews are mostly from plus magazine, the London Mathematical Society's newsletter, the Notices of the American Mathematical Society, the Reviews site of the Mathematical Association of America, and the 'bookshelf' section of American Scientist. They are generally pdf files and will open in a new window. Some of the AMS reviews are extended essays, including images, and can be relatively large files (a size indication is given where appropriate).
If you know of an additional online review of any of the books here (or would like to contribute one) I would be very glad to include a link to it.
Occasionally there is a legitimate free electronic version of a book. I link to this with the word Ebook. Again, I'd be very pleased to know of more. Increasingly books have webpages supporting them (sometimes even Wikipedia entries) and these are linked with the word Webpage.
I have grouped the entries below into, necessarily somewhat arbitrary, categories as follows:
Collections, Dictionaries, Encyclopedias
(You may actually be one of the books in the 'Research level' category: David Savitt lets you find out here.)
Collections, Dictionaries, Encyclopedias
Barry Cipra, What's Happening in the Mathematical Sciences, vol. 1 , American Mathematical Society, 1993.
Barry Cipra (ed. Paul Zorn), What's Happening in the Mathematical Sciences, vol. 2, American Mathematical Society, 1994.
——— , What's Happening in the Mathematical Sciences, vol. 3, Americal Mathematical Society, 1996.
——— , What's Happening in the Mathematical Sciences, vol 4, Americal Mathematical Society, 1999.
——— , What's Happening in the Mathematical Sciences, vol. 5, American Mathematical Society, 2002.
Pierre Colmez and J.P. Serre (eds.), Grothendieck-Serre Correspondence: Bilingual Edition, American Mathematical Society, 2004. Review
Dana Mackenzie and Barry Cipra, What's Happening in the Mathematical Sciences, vol. 6, American Mathematical Society, 2006.
Dana Mackenzie, What's Happening in the Mathematical Sciences, vol. 7, American Mathematical Society, 2009.
——— , What's Happening in the Mathematical Sciences, vol. 8, American Mathematical Society, 2011.
——— , What's Happening in the Mathematical Sciences, vol. 9, American Mathematical Society, 2013.
Yuri I. Manin, Mathematics as Metaphor: Selected Essays of Yuri I. Manin, American Mathematical Society, 2008.
Peter M. Neumann, The Mathematical Writings of Evariste Galois (Heritage of European Mathematics) , European Mathematical Society, 2011. Review
Terence Tao, Structure and Randomness: Pages from Year One of a Mathematical Blog, American Mathematical Society, 2009. Review
——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 1, American Mathematical Society, 2009.
——— , Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 2, American Mathematical Society, 2009.
——— , An Epsilon of Room, I: Real Analysis: Papers from Year Three of a Mathematical Blog, American Mathematical Society, 2011.
——— , An Epsilon of Room, II: 2: Papers from Year Three of a Mathematical Blog, American Mathematical Society, 2011. Review
——— , Compactness and Contradiction, American Mathematical Society, 2013.
Stanisław Ulam, The Scottish Book, publ. by Los Alamos, N.M. : S. Ulam, 1957. Ebook
William Frucht (ed.), Imaginary Numbers: An Anthology of Marvellous Mathematical Stories, Diversions, Poems and Musings, John Wiley & Sons,1999. Review
Dora Musielak, Sophie's Diary: A Historical Fiction, AuthorHouse, 2004.
Chris Pearson, Proof of Death, published on Kindle via Amazon Media EU S.à r.l., 2012.
History of mathematics (including historical reprints)
William J. Adams, The Life and Times of the Central Limit Theorem, 2nd edition , American Mathematical Society, 2010. Review
Marlow Anderson, Victor Katz and Robin Wilson (eds.), Sherlock Holmes in Babylon and Other Tales of Mathematical History, The Mathematical Association of America, 2004. Review, Review
——— , ——— and ——— (eds.), Who Gave you the Epsilon? & Other Tales of Mathematical History, The Mathematical Association of America, 2004. Review
Petr Beckmann, A History of Pi, 3rd ed., Saint Martin's Press Inc., 1976.
Janet Beery and Jacqueline Stedall (eds.), Thomas Harriot's Doctrine of Triangular Numbers: The Magisteria Magna, European Mathematics Society, 2008. Review
William Berlinghoff and Fernando Gouvêa, Math through the Ages: A Gentle History for Teachers and Others, Oxton House Publishers, 2002. Review
Oliver Byrne, Byrne, Six Books of Euclid: Facsimile of the famous first edition of 1847, Taschen, 2010. Review
Bruce Chandler and Wilhelm Magnus, The History of Combinatorial Group Theory: A Case Study in the History of Ideas, Springer, 1982
William Chauvanet, Binomial Theorem and Logarithms, BiblioBazaar, 2008.
Brian Clegg, Brief History of Infinity: The Quest to Think the Unthinkable, Robinson Publishing, 2003. Review
Alex D.D. Craik, Mr Hopkins' Men: Cambridge Reform and British Mathematics in the 19th Century, Springer, London 2007. Review
Alan Cromer, Uncommon Sense: The Heretical Nature of Science, Oxford University Press, 1995.
Michael J. Crowe, A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, Dover 2003.
Olivier Darrigol, Worlds of Flow: A history of hydrodynamics from the Bernoullis to Prandtl, Oxford Univ. Press 2005. Review
Joseph W. Dauben and Christoph J. Scriba (eds.), Writing the History of Mathematics - Its Historical Development, Birkhauser, 2002. Review
Martin Davis, The Universal Computer: The Road from Leibniz to Turing, W. W. Norton, 2000. Review
John Derbyshire, Unknown Quantity: A Real and Imaginary History of Algebra, Plume Books, 2007. Review
Keith Devlin, The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern, Basic Books, 2010. Review
A.W.F. Edwards, Pascal's Arithmetical Triangle: The Story of a Mathematical Idea, Johns Hopkins University Press, 2002.  Review
John Fauvel, Raymond Flood and Robin Wilson, (eds.), Oxford Figures: 800 Years of the Mathematical Sciences, Oxford University Press, 2000.  Review
José Ferreirós and Jeremy Gray, The Architecture of Modern Mathematics: Essays in History and Philosophy, Oxford University Press, 2006. 
J.V. Field and Jeremy Gray, The Geometrical Work of Girard Desargues, Springer-Verlag, New York, 1987.
——— , The Invention of Infinity: Mathematics and Art in the Renaissance, Oxford University Press, 1997. Review
Raymond Flood, Adrian Rice and Robin Wilson (eds.), Mathematics in Victorian Britain, Oxford University Press, 2011.
Jeremy J. Gray, The Hilbert Challenge: A Perspective on Twentieth Century Mathematics, Oxford University Press, 2000. Review, Review
——— , Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space, MIT Press, 2004. Review, Review
——— , Plato's Ghost: The Modernist Transformation of Mathematics, Princeton University Press, 2008. Review, Review, Review
Thomas Hawkins, Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926, Springer-Verlag, New York, 2000. Review
Ioan James, Driven to Innovate: A Century of Jewish Mathematicians and Physicists: A Century of Mathematicians and Physicists, Peter Lang 2009. Review
Ellen Kaplan and Robert Kaplan, Hidden Harmonies: The Lives and Times of the Pythagorean Theorem , Bloomsbury Press, 2011. Review
——— , Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook, Princeton University Press, 2007.  Review
——— , Mathematical Thought from Ancient to Modern Times: Vol 1, Oxford University Press, 1990 re-edition, also Vol 2 and Vol 3.
Edna Ernestine Kramer, The Nature and Growth of Modern Mathematics, Princeton University Press, 1983.
Richard Laubenbacher and D. Pengelley, Mathematical Expeditions: Chronicles by the Explorers, Springer New York, 2000.  Review
Olli Lehto, Mathematics Without Borders: A History of the International Mathematical Union, Springer, 1998. Review
Reviel Netz (editor and translator), The Works of Archimedes: Volume 1, The Two Books On the Sphere and the Cylinder: Translation and Commentary, Cambridge University Press, 2004. Review (1.8MB)
Peter Roquette, The Brauer-Hasse-Noether Theorem in Historical Perspective, Springer, 2004.  Review
Walter William Rouse Ball, A History of the Study of Mathematics at Cambridge , Cambridge University Press, 2009 facsimile reprint. Review
Winfried Scherlau and Hans Opolka (transl. W.K. Bühler and G. Cornell) From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical Development, Springer-Verlag, New York, 2010.  Review
Muriel Seltman and Robert Goulding (eds.), Thomas Harriot's Artis Analyticae Praxis: An English Translation with Commentary, Springer Verlag, 2007. Review
Jacqueline A. Stedall, The Arithmetic of Infinitesimals: John Wallis 1656, Springer, 2004.  Review
——— , From Cardano's Great Art to Lagrange's Reflections: Filling a Gap in the History of Algebra, European Mathematical Society, 2011.
——— , The History of Mathematics: A Very Short Introduction, Oxford University Press, 2012. Review
John Stillwell, Mathematics and Its History, 3rd edition, Springer, 2010.
Dirk J. Struik, A Concise History of Mathematics, Fourth Revised Edition], Dover Publications, 1987. Review
Frank J. Swetz, Mathematical Expeditions: Exploring Word Problems across the Ages, The Johns Hopkins University Press, 2012. Review
——— , Poor Robin's Prophecies: A curious Almanac, and the everyday mathematics of Georgian Britain, Oxford University Press, 2012.
——— and John J. Watkins (eds.), Combinatorics: Ancient & Modern, OUP, 2013.
Links to Review or to Obituary often provide a first rate summary of the subject's life and achievements.
Collections of biographies appear separately under The Profession of Mathematics.
[Abel, Niels Henrik] Arild Stubhaug (translated R. Daly), Niels Henrik Abel and his Times: Called Too Soon by Flames Afar, Springer-Verlag, Berlin, 2000. Review
[Albert, Abraham Adrian] Nancy E. Albert, A3 & His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics, iUniverse, Inc., 2005. Review
[Babbage, Charles] Doron Swade, The Cogwheel Brain: Charles Babbage and the quest to build the first computer, Little, Brown and Company, 2000. Review
[Banach, Stefan] Emilia Jakimowicz and Adam Miranowicz (eds.), Stefan Banach: Remarkable Life, Brilliant Mathematics, American Mathematical Society, 3rd edition, 2011.
[Banach, Stefan] Roman Kaluza (transl. A. Kostant and Wojbor A. Woyczynski), Through a Reporter's Eyes: The Life of Stefan Banach, Birkhauser, 2005.
[Cayley, Arthur] Tony Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age , John Hopkins University Press, 2006. Review, Review
[Clifford, William and Lucy] M. Chisholm, Such Silver Currents: The Story of William and Lucy Clifford, 1845-1929 , Lutterworth Press, 2002. Review
[Coxeter, Donald] Siobhan Roberts, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Profile Books Ltd, 2007. Review, Review
[Dee, John] Benjamin Wooley, The Queen's Conjuror: The Science and Magic of Dr. Dee, Flamingo, new edition 2002. Review
[Erdős, Paul] Paul Hoffman, The Man Who Loved Only Numbers: the Story of Paul Erdős and the Search for Mathematical Truth, Fourth Estate, new edition 1999. Review
[Erdős, Paul] Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdős, Touchstone, 2000. Review
[Kovalevskaia, Sofia] Ann Hibner Köblitz, A Convergence of Lives: Sofia Kovalevskaia: Scientist, Writer, Revolutionary, Rutgers University Press, reprint edition 1993.
[Lie, Sophus] Arild Stubhaug (translated R. Daly), The Mathematician Sophus Lie: It was the Audacity of My Thinking, Springer, paperback edition 2010. Review
[Mosteller, Charles Frederick] Frederick Mosteller, The Pleasures of Statistics: The Autobiography of Frederick Mosteller, Springer, 2010. Review
[Ramanujan, Srivivasa] Robert Kanigel, The Man Who Knew Infinity: a Life of the Genius Ramanujan, Abacus, new edition 1992.
[Smale, Stephen] Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, AMS, 2000. Review
[Sylvester, James Joseph] Karen H. Parshall, James Joseph Sylvester: Jewish Mathematician in a Victorian World, The Johns Hopkins University Press, 2006.  Review
[Turing, Alan Mathison] David Leavitt, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer, W. W. Norton 2005. Review, Review
[Volterra, Vito] Judith R. Goodstein, The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940, American Mathematical Society, 2007. Review (2.8MB)
[Wiener, Norbert] Flo Conway and Jim Siegelman, Dark Hero of the Information Age: In Search of Norbert Wiener - Father of Cybernetics, Basic Books, 2005. Review
The profession of mathematics
E. Bell, Men of Mathematics, Simon & Schuster Inc, 1986.
William Byers, How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics, Princeton University Press, 2007. Review
Alexandre V. Borovik, Mathematics Under the Microscope: Notes on Cognitive Aspects of Mathematical Practice, American Mathematical Society, 2010. Review, Review
Richard Courant and Herbert Robbins, revised by Ian Stewart, What is Mathematics?: An Elementary Approach to Ideas and Methods, Oxford University Press Inc, 2nd Revised, 1996. Review
Paul R. Halmos, I Want to Be a Mathematician: An Automathography, Springer, New York, 1985.
Reuben Hersh and Vera John-Steiner, Loving and Hating Mathematics: Challenging the Myths of Mathematical Life, Princeton University Press, 2010. Review
Nicolas Higham, Handbook of Writing for the Mathematical Sciences, Society for Industrial and Applied Mathematics; 2 edition, 1998.
Ioan James, Remarkable Mathematicians: From Euler to von Neumann, Cambridge University Press, 2003. Review, Review
Donald E. Knuth, Tracy Larrabee and Paul M. Roberts, Mathematical Writing, The Mathematical Association of America, 1996.
——— , Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical, The Mathematical Association of America, 2002. Review, Review
——— ,A Mathematician's Survival Guide: Graduate School and Early Career Development, American Mathematical Society, 2003. Review
——— , Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical, The Mathematical Association of America, 2006. Review
——— , The Proof is in the Pudding: The Changing Nature of Mathematical Proof, Springer, 2011.
Charlene Morrow and Teri Perl (eds.), Notable Women in Mathematics: A Biographical Dictionary, Greenwood Press, 1998. Review
Luetta Reimer and Wilbert Reimer, Mathematicians are People Too: Stories from the Lives of Great Mathematicians, vol. 1, and Vol 2, Seymour (Dale) Publications, 1998. Review
Norbert Wiener, I Am a Mathematician, Victor Gollanz, London, 1956.
Robin V. Young (ed.), Notable Mathematicians from Ancient Times to the Present, Gale, 1998.
Psychology, Sociology, Philosophy
Robyn Arianrhod, Einstein's Heroes: Imagining the World Through the Language of Mathematics, Icon Books, 2004. Review
Marcia Ascher, Mathematics Elsewhere: An Exploration of Ideas Across Cultures, Princeton University Press, 2002. Review
Ehrhard Behrends, Nuno Crato and José Francisco Rodrigues (Editors), Raising Public Awareness of Mathematics, Springer, 2012
James Robert Brown, Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures, Routledge, 2nd edition, 2008. Review
Stephen Ceci and Wendy Williams, The Mathematics of Sex: How Biology and Society Conspire to Limit Talented Women and Girls, Oxford University Press, 2009.
Jean-Pierre Changeux and Alain Connes, Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998. Transl. by Malcolm DeBevoise.
E. Brian Davis, Why Beliefs Matter: Reflections on the Nature of Science , Oxford University Press, 2010. Review
Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics, revised edition, Oxford University Press, USA, 2011. Review
Keith Devlin, The Maths Gene: Why Everyone Has It, But Most People Don't Use It, Phoenix, new edition 2001. Review, Review, Review
A. K. Dewdney, A Mathematical Mystery Tour: Discovering the Truth and Beauty of the Cosmos, John Wiley & Sons, 1999. Review
Apostolos Doxiadis and Barry Mazur, Circles Disturbed: The Interplay of Mathematics and Narrative, Princeton University Press, 2012. Review
Bonnie Gold and Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy, Mathematical Association of America, 2008. Review
John Horgan, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Helix Books, 1996. Review
Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, edited by Worrall and Zahar, Cambridge University Press, 1976. 
George Lakoff and Rafael E. Núñez, Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being, Basic Books, 2000. Review, Review
Margaret A. M. Murray, Women Becoming Mathematicians: Creating a Professional Identity in Post-world War II America, MIT Press, 2000. Review
Roland Omnès, Converging Realities: Toward a Common Philosophy of Physics and Mathematics, Princeton University Press, 2004. Review
John Allen Paulos, Mathematics and Humour, University of Chigago Press, 1990.
Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford Paperbacks; New Ed, 1999. Review
——— , Shadows of the Mind: A Search for the Missing Science of Consciousness, Vintage, 1995. Review, Review, Review, Rebuttals
Valerie Walkerdine, Counting Girls Out: Girls and Mathematics, Routledge, 2nd edition, 1998.
Mathematical mountains: popular accounts of landmark problems/solutions
John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, Plume Books, 2004. Review
Keith Devlin, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, Basic Books, 2002. Review, Review
Underwood Dudley, The Trisectors, 2nd edition, Mathematical Association of America, 1996.
Lance Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible, Princeton University Press, 2013. Review, Review
Mario Livio, The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, Souvenir Press Ltd, new edition, 2007. Review, Review
Piergiorgio Odifreddi, The Mathematical Century: The 30 Greatest Problems of the Last 100 Years, transl. Arturo Sangalli, Princeton University Press, (new edition) 2006. Review
Donal O’Shea, The Poincaré Conjecture: In Search of the Shape of the Universe , Walker, 2007. Review (2.8MB), Review
Peter Pesic, Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, MIT Press, 2003. Review
Mark Ronan, Symmetry and the Monster: One of the Greatest Quests of Mathematics, Oxford University Press, 2006.  Review, Review, Review
George Szpiro, Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World, John Wiley & Sons, 2003.  Review, Review
——— , Poincare's Prize: The Hundred-year Quest to Solve One of Math's Greatest Puzzles , Dutton/Signet, 2007. Review (2.8MB)
Robin Wilson, Four Colors Suffice: How the Map Problem Was Solved (Revised Color Edition), Princeton University Press, 2013.  Review, Review, Review
Benjamin H. Yandell, The Honors Class: Hilbert's Problems and Their Solvers, AK Peters, 2001. Review, Review
Introductions to mathematical topics accessible for non-professionals
Colin Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, 2004.  Review
———, Elliptic Tales: Curves, Counting, and Number Theory, Princeton University Press, 2012.
Tomaso Aste and Denis Weaire, The Pursuit of Perfect Packing, Second Edition, CRC Press, 2008.
V.K. Balakrishnan, Graph Theory: Including Hundreds of Solved Problems (Schaum), McGraw-Hill Publishing Co., 1997.
Robert B. Banks, Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics, Princeton University Press, new edition 2013. Review
Ehrhard Behrends (transl. D. Kramer), Five-Minute Mathematics, American Mathematical Society, 2008.
John Bryant and Chris Sangwin, How Round Is Your Circle?: Where Engineering and Mathematics Meet, Princeton University Press, 2011. Review
Chris Caldwell and G. L. Honaker, Jr., Prime Curios, BookSurge, 2009.
John L Casti, Five Golden Rules: Great Theories of 20th Century Mathematics and Why They Matter, John Wiley, 1997. 
William J. Cook, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, Princeton University Press, 2012. Review, Review
Keith Devlin, The Language of Mathematics: Making the Invisible Visible, W.H.Freeman & Co Ltd, 2000. Review
Underwood Dudley, Mathematical Cranks, The Mathematical Association of America, 1996.
William Dunham, Journey Through Genius: Great Theorems of Mathematics, John Wiley & Sons, 1990. 
——— , The Genius of Euler: Reflections on His Life and Work , The Mathematical Association of America, 2007.  Review
Richard Elwes, How to Build a Brain: And 34 Other Really Interesting Uses of Mathematics, Quercus Publishing Plc, 2011. Review
Paulus Gerdes, Geometry from Africa. Mathematical and educational explorations, The Mathematical Association of America, 1999. Review
Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel, W. W. Norton & Company, 2005. Review, Review
———, Nonplussed: Mathematical Proof of Implausible Ideas, Princeton University Press, 2007. Review, Review
———, The Irrationals: A Story of the Numbers You Can't Count On, Princeton University Press, 2012. Review
———, Nets, Puzzles, and Postmen: An exploration of mathematical connections, Oxford University Press, 2009. Review
Peter Hilton, Derek Holton, and Jean Pedersen, Mathematical Vistas: From a Room with Many Windows, Springer-Verlag, New York, 2002. Review
——— and Jean Pedersen, with illustrations by Sylvie Donmoyer, A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics, Cambridge University Press, 2010. Review
Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, 1996. [55, 84]
H.E. Huntley, The Divine Proportion: A Study in Mathematical Beauty, Dover Publications, 1970. 
Dan Kalman, Uncommon Mathematical Excursions: Polynomia and Related Realms, The Mathematical Association of America, 2009.
Richard J. Lipton, The P=NP Question and Gödel's Lost Letter, Springer, New York, 2010.
Mario Livio, The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty, Headline Review, new edition 2003. Review, Review
Dana Mackenzie, The Universe in Zero Words: The Story of Mathematics as Told through Equations, Princeton University Press, 2012. Review
Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen), Farrar, Straus and Giroux, 2003. Review
T.S. Michael, How to Guard an Art Gallery and Other Discrete Mathematical Adventures, The Johns Hopkins University Press, 2009.
Paul J. Nahin, Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills, Princeton University Press, 2006.  Review, Review
John Allen Paulos, A Mathematician Reads the Newspaper: Making Sense of the Numbers in the Headlines, Basic Books, 1999. Review
———, A Mathematician Plays the Market, Penguin, 2004.
Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Vintage, 2005.  Review
Cliff Pickover, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling, 2009.
Alfred S. Posamentier and Ingmar Lehmann, Pi: A Biography of the World's Most Mysterious Number, Prometheus, 2004.
———, The Fabulous Fibonacci Numbers, Prometheus, 2007.
Alfred S. Posamentier, The Pythagorean Theorem: The Story of Its Power and Beauty, Prometheus, 2010.
William Poundstone, Prisoner's Dilemma: John Von Neumann, Game Theory and the Puzzle of the Bomb, Anchor Booksn 1993. Review
George Pólya, How to Solve it: A New Aspect of Mathematical Method, Penguin, new edition 1990. Review
Constance Reid, From Zero to Infinity: What Makes Numbers Interesting, A K Peters/CRC Press; 5th revised edition, 2006. Review, Review
David S. Richeson, Euler's Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press, 2008. Review
Anne Rooney, 50 Amazing Things Kids Need to Know About Mathematics, Quercus Publishing Plc, 2011. Review
Lionel Salem, Frederic Testard and Coralie Salem, The Most Beautiful Mathematical Formulas: An Entertaining Look at the Most Insightful, Useful and Quirky Theorems of All Time, John Wiley & Sons, 1997.
Sherman Stein, How the Other Half Thinks: Adventures in Mathematical Reasoning, McGraw-Hill, 2001. Review
Hugo Steinhaus, One Hundred Problems in Elementary Mathematics, Dover Publications, 1990.
Ian Stewart, Does God Play Dice?: The New Mathematics of Chaos, 2nd edition, Penguin, 1997.
John Stillwell, Roads to Infinity: The Mathematics of Truth and Proof, AK Peters, 2010. Review
Steven Strogatz, The Joy of X: A Guided Tour of Math, from One to Infinity, Eamon Dolan/Houghton Mifflin Harcourt, 2012.
Terence Tao, Solving Mathematical Problems: A Personal Perspective, Oxford University Press, 2nd edition 2006. Review, Review
Matthew Watkins, The Mystery of the Prime Numbers: Secrets of Creation v. 1, The Inamorata Press, 2010. Review
——— , The Enigma of the Spiral Waves: Secrets of Creation v. 2, The Inamorata Press, 2011.
David Wells, You Are a Mathematician, Penguin, London, 1995.
——— , Prime Numbers: The Most Mysterious Figures in Math, John Wiley & Sons Inc, 1995. 
Robert, M. Young, Excursions in Calculus: An Interplay of the Continuous and the Discrete, Mathematical Association of America, 1996. 
More specialised introductions to mathematical topics
M. Ya. Antimirov, A. A. Kolyshkin and Rémi Vaillancourt, Complex Variables, Academic Press, San Diego, 1998.
David L. Applegate, Robert E. Bixby, Vašek Chvátal and William J. Cook, The Traveling Salesman Problem: A Computational Study, Princeton University Press, 2006.  Review
Jörg Arndt and Christoph Haenel (translated, C. Lischka and D. Lischka), Pi - Unleashed , Springer, 2000.
Arthur T. Benjamin and Jennifer J. Quinn, Proofs that Really Count: The Art of Combinatorial Proof, The Mathematical Association of America, 2003.  Review
K.G. Binmore, The Foundations of Analysis: A Straightforward Introduction: Book 1 Logic, Sets and Numbers, Cambridge University Press, 1981.
——— , The Foundations of Analysis: A Striaghtforward Introduction: Book 2 Topological Ideas, Cambridge University Press, 1981. 
Miklós Bóna, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory, 2nd edition, World Scientific Publishing, 2006. Review
Jonathan M. Borwein, David H. Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2008.  Review, Review, Review
David M. Bressoud, Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture, Cambridge University Press, 1999. Review
——— , A Radical Approach to Lebesgue's Theory of Integration, Cambridge University Press, 2008.  Review
Edward B. Burger and Robert Tubbs, Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory, Springer, 2004.  Review
B.A. Davey and H.A. Priestly, Introduction to Lattices and Order, Cambridge University Press, 1990.
William Feller, An Introduction to Probability Theory and Its Applications: vol. 2 (Probability & Mathematical Statistics), John Wiley, Canada, 1971.
Torkel Franzén, Godel's Theorem: An Incomplete Guide to Its Use and Abuse, A.K. Peters, 2005. Review, Review
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, W.H.Freeman & Co Ltd, 1979. [14, 187]
Gary Gordon and Jennifer MacNulty, Matroids: A Geometric Introduction, Cambridge University Press, 2012
Ronald Graham, Donald Knuth and Oren Patashnik, Concrete Mathematics: Foundation for Computer Science, Addison Wesley, 2nd ed., 1994. Ebook
Jack E. Graver, Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, The Mathematical Association of America, 2001.  Review, Review
Ernst Hairer and Gerhard Wanner, Analysis by its History, Springer, 1996.
G.H. Hardy and E.W. Wright (with additional material by D.R. Heath-Brown, J.H. Silverman and A. Wiles), An Introduction to the Theory of Numbers, OUP, 6th edition, 2008.
Ann Hirst and David Singerman, Basic Algebra and Geometry, Prentice Hall, 2000.
Kevin Houston, How to Think Like a Mathematician: A Companion to Undergraduate Mathematics, Cambridge University Press, 2009.
Arthur Jones, Sidney A. Morris and Kenneth R. Pearson, Abstract Algebra and Famous Impossibilities, Springer-Verlag, New York, 1991.
Gareth A. Jones and David Singerman, Complex Functions: An Algebraic and Geometric Viewpoint, Cambridge University Press, 1987.
Stasys Jukna, Extremal Combinatorics: With Applications in Computer Science, Springer, 2nd edition, 2011. 
——— , Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, American Mathematical Society, 2010. Review
Melzak, Z.A., Companion to Concrete Mathematics: Two Volumes Bound as One: Volume I: Mathematical Techniques and Various Applications, Volume II: Mathematical Ideas, Modeling and Applications, Dover Publications, 2007. Review
Dwight Neuenschwander, Emmy Noether's Wonderful Theorem, The Johns Hopkins University Press, 2010.
Christos Papadimitriou and Kenneth Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Dover Publications (New edition) 2000. [62, 168,185]
Charles Petzold, The Annotated Turing: A Guided Tour Through Alan Turing's Historic Paper on Computability and the Turing Machine, Wiley Publishing, Inc., 2008. Review, Review
Harriet Pollatsek, Lie Groups: A Problem-Oriented Introduction via Matrix Groups, Mathematical Association of America, 2009. Review
H.E. Priestly, Introduction to Complex Analysis, 2nd edition, Oxford University Press, 2003.
Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press, 1988.
——— and Balázs Szendrői, Geometry and Topology, Cambridge University Press, 2005.
——— and Olga Tabachnikova, Topics in Group Theory, Springer, London, 2000.
Kenneth Stephenson, Introduction to Circle Packing: The Theory of Discrete Analytic Functions, Cambridge University Press, 2005. [130, 179] Review, Review
J. Michael Steele, The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities, Mathematical Association of America, 2004.  Review
Thomas M. Thompson, From Error-Correcting Codes through Sphere Packings to Simple Groups, Mathematical Association of America, 2004.  Review
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