A more thorough subject by subject list is on the Mathematics page.

## Preschool (Arithmetic)

Feel free to skip Preschool if you can add and multiply with any amount of proficiency.

Quick Arithmetic by Robert Carman

• All the Math You'll Ever Need: A Self-Teaching Guide by Slavin (All the *Arithmetic* you'll ever need)
• Speed Mathematics Simplified (Dover Books) by Edward Stoddard
• Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks by Benjamin
• The Mental Calculator's Handbook by Fountain and Koningsveld (More depth than the above, basic to intermediate level)
• Dead Reckoning: Calculating Without Instruments by Doerfler (Warning: More advanced than the above, covers logarithms and trigonometric functions and their inverses, may require some calculus knowledge for maximum enjoyment)[site]

• Algebra by Gelfand and Shen
• Functions and Graphs by Gelfand, Glagoleva, and Shnol
• The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
• Trigonometry by Gelfand and Saul
• Kiselev's Geometry: Book I. Planimetry & Book II. Stereometry
• Basic Mathematics by Lang and/or Precalculus with Unit Circle Trigonometry by Cohen

## High School

• Euclid's Elements
• Geometry Revisited by Coxeter
• Elementary Calculus: An Infinitesimal Approach by H. Jerome Keisler
• Calculus Vol I & II by Apostol or Calculus by Spivak
• Linear Algebra and Its Applications by Strang
• Ordinary Differential Equations by Tenenbaum and Pollard
• A Primer of Abstract Mathematics by Ash
• Conjecture and Proof by Laczkovich
• Proofs from THE BOOK by Aigner and Ziegler

## University

• Elements of Set Theory by Enderton
• A Mathematical Introduction to Logic by Enderton
• Generatingfunctionology by Wilf
• Linear Algebra by Shilov
• Geometry by Brannan
• Complex Analysis by Bak
• Visual Complex Analysis by Needham
• Probability and Random Processes by Grimmett & Stirzaker
• Applied Partial Differential Equations by Haberman
• Partial Differential Equations by Strauss
• Numerical Analysis by Burden
• Matrix Computations by Golub and Van Loan
• Algebra by Artin
• Topics in Algebra by Herstein
• The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by Steele
• Inequalities by Hardy, Littlewood, and Polya
• Topology by Munkres[Errata 1] and Counterexamples in Topology by Steen & Seebach
• Principles of Mathematical Analysis by Rudin[Errata 2]
• Counterexamples in Analysis by Gelbaum and Olmsted
• A Course of Modern Analysis by Whittaker and Watson and Special Functions by Wang and Guo
• An Introduction to the Theory of Numbers by Niven, Zuckerman, and Montgomery[Errata 3]
• Differential Geometry of Curves and Surfaces by Do Carmo[Errata 4]
• Analysis on Manifolds by Munkres
• Ordinary Differential Equations by Arnold
• Algebraic Topology by Hatcher
• Fourier Analysis; Complex Analysis; Real Analysis: Measure Theory, Integration, and Hilbert Spaces; Functional Analysis by Stein
• Theoretical Numerical Analysis: A Functional Analysis Framework by Atkinson and Han
• An Introduction to Probability Theory and Its Applications Vol. 1&2 by Feller
• Partial Differential Equations by Jost
• Basic Algebra I & II by Jacobson
• Modern Graph Theory by Bollobás
• A Classical Introduction to Modern Number Theory by Ireland and Rosen
• Introduction to Analytic Number Theory by Apostol
• Enumerative Combinatorics by Stanley

## Historical

• e: the Story of a Number by Maor
• Trigonometric Delights by Maor
• MY BRAIN IS OPEN: The Mathematical Journeys of Paul Erdos by Schechter
• A Mathematician Apology by Hardy
• I Want to be a Mathematician: An Automathography by Halmos
• The Apprenticeship of a Mathematician by Andre Weil
• The Man Who Knew Infinity: A Life of the Genius Ramanujan by Kanigel
• The Way I Remember It by Walter Rudin
• The Volterra Chronicles: The Life and Times of an Extraordinary Mathematician 1860-1940 by Goodstein
• Hilbert - Courant by Reid
• The Honors Class: Hilbert's Problems and Their Solvers by Yandell
• Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Ronan
• Gauss: A Biographical Study by Bühler

### Textbooks and heavier works

• A History of Mathematics by Katz
• A History of Mathematics by Boyer and Merzbach
• Mathematics and Its History by Stillwell
• A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Crowe
• Zermelo's Axiom of Choice: Its Origins, Development, and Influence (Dover Books) by Gregory H. Moore
• A History of Algebraic and Differential Topology, 1900 - 1960 by Dieudonne
• History of Topology by James
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869 - 1926 by Hawkins
• From Error Correcting Codes Through Sphere Packings to Simple Groups by Thompson
• History of Banach spaces and Linear Operators by Pietch

### Original influential works, papers, and books of interest

• A History of Greek Mathematics by Heath
• The Works of Archimedes by Heath
• Ptolemy's Almagest
• On the Revolutions of Heavenly Spheres by Nicolaus Copernicus
• The Principia: Mathematical Principles of Natural Philosophy by Isaac Newton, Cohen and Whitman (Translators)
• Elements of Algebra by Leonhard Euler; notes added by Johann Bernoulli, and additions by Joseph-Louis Lagrange
• Introductio in analysin infinitorum (Introduction to Analysis of the Infinite) by Leonhard Euler
• Institutiones calculi differentialis (Foundations of Differential Calculus), Institutionum calculi integralis (Foundations of Integral Calculus) by Leonhard Euler
• Disquisitiones Arithmeticae by Carl Gauss
• An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole
• The Mathematical Theory of Communication by Claude Shannon