This post is taken (with some modifications from an answer I gave at quora.com .
Classic books or classics may refer to great and historically important books , or to books widely popular , read and used ,or both . I will try to mention both types of books.
I will cite first a number of books which I think are of primary importance in the history of mathematics , and therefore are generally regarded as classics . This is not a exhaustive list .
Let’s start with some books from Antiquity :
Moving a few centuries later to modern times :
- The Compendious Book on Calculation by Completion and Balancing , by Muhammad ibn Musa al-Khwarizmi .
- Ars Magna (Gerolamo Cardano)
- La Géométrie by René Descartes . The image below is a free image from archive.org .
- Philosophiæ Naturalis Principia Mathematica by Isaac Newton .
- Introductio in analysin infinitorum , by Leonhard Euler .
- Mathematical papers by Joseph-Louis Lagrange ,such as “Reflections on the algebraic solutions of equations”.
- Mathematical papers and works by Pierre-Simon Laplace , which can be found in his collected works.
- Disquisitiones Arithmeticae and General investigations of curved surfaces of 1827 and 1825; tr. with notes and a bibliography by James Caddall Morehead and Adam Miller Hiltebeitel. , by Carl Friedrich Gauss . The image below is from Wikipidia :
- An Investigation of the Laws of Thought , by George Boole .
- The mathematical works of Bernhard Riemann .
- Analysis Situs (paper) by Henri Poincaré .
- Leçons sur l’intégration et la recherche des fonctions primitives, professées au Collège de France : Lebesgue, Henri Léon, 1875-1941 : Free Download & Streaming : Internet Archive
- The Foundations of Geometry : Hilbert, David, 1862-1943 : Free Download & Streaming : Internet Archive
- A short account of the history of mathematics : Ball, W. W. Rouse (Walter William Rouse), 1850-1925 : Free Download & Streaming : Internet Archive
- Methods of Mathematical Physics , by David Hilbert and Richard Courant .
- The Absolute Differential Calculus : Free Download & Streaming : Internet Archive
- A Course of Pure Mathematics and An Introduction to the Theory of Numbers , by G. H. Hardy .
- Some books and papers by Albert Einstein are related to (breakthroughs in) physics , other deal with physics and mathematics .
- The Theory of Spinors , by Élie Cartan .
- The Theory of Functions : E.C. Titchmarsh : Free Download & Streaming : Internet Archive
- The Classical Groups , by Hermann Weyl .
- A Treatise on the Theory of Bessel Functions : G.N. Watson : Free Download & Streaming : Internet Archive
Some recent modern and well known math books that may be regarded as classics :
- Éléments de mathématique , by Nicolas Bourbaki . The image below is a free image of the first edition of Bourbaki’s book about set theory (in French) from Wikipedia .
- Introduction to Geometry and Non-Euclidean Geometry , by Harold Scott MacDonald Coxeter .
- Theory of Lie groups by Claude Chevalley .
- Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics): Milton Abramowitz, Irene A. Stegun: 9780486612720: Amazon.com: Books
- Mathematical Methods of Classical Mechanics , by Vladimir Arnold .
- Topology, by James Munkres .
- Group Theory and Its Application to Physical Problems (Dover Books on Physics): Morton Hamermesh, Physics: 9780486661810: Amazon.com: Books
- Elementary Theory of Analytic Functions of One or Several Complex Variables (Dover Books on Mathematics): Henri Cartan: 9780486685434: Amazon.com: Books
- Lie Groups: Beyond an Introduction: Anthony W. Knapp: 9780817642594: Amazon.com: Books
- Amazon.com: Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) (International Series in Pure & Applied Mathematics) (9780070542358): Walter Rudin: Books
- Categories for the Working Mathematician by Saunders Mac Lane .
- Amazon.com: Michael Atiyah Collected Works: 6-Volume Set (9780198520948): Michael Atiyah: Books
- Modular Elliptic Curves and Fermat’s Last Theorem by Andrew Wiles (Wiles’ proof of Fermat’s Last Theorem ) .
- Noncommutative Geometry , by Alain Connes .
- The Road to Reality , by Roger Penrose .
See also the following links :