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)<sup>[[http://www.myreckonings.com/Dead_Reckoning/Dead_Reckoning.htm site]]</sup>
==Grade School==
*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<ref>https://www.math.wisc.edu/~keisler/calc.html</ref>
*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<ref>http://www.math.upenn.edu/~wilf/DownldGF.html</ref>
*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<ref group="Errata">http://www.math.toronto.edu/drorbn/classes/0405/Topology/etc/MunkresErrata.html</ref> and Counterexamples in Topology by Steen & Seebach
*Principles of Mathematical Analysis by Rudin<ref group="Errata">http://www.jirka.org/rudin-errata.html</ref>
*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<ref group="Errata">http://www-personal.umich.edu/~hlm/nzm/</ref>
*Differential Geometry of Curves and Surfaces by Do Carmo<ref group="Errata">http://www.math.umn.edu/~tlawson/5378/docarmo_errata.pdf</ref>
* Analysis on Manifolds by Munkres
*Ordinary Differential Equations by Arnold
*Algebraic Topology by Hatcher<ref>http://www.math.cornell.edu/~hatcher/AT/ATpage.html</ref>
*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 ==

=== Light reading ===
* 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
== Errata ==
<references group="Errata" />
== Public Domain Material ==
<references />
