Open-access textbooks

This page includes a list of mathematics textbooks that can be freely accessed online. The books are broken down by subject and listed alphabetically within. Each book includes a link to the text in addition to the license(s) under which they are published.

Note that not all of these books are "free" as in "freedom" (c.f. What is free software?), but all can be accessed free of cost. If you are unsure about the restrictions of any given license, you can follow the link and read more.

Please let me know if any of these links are out-of-date so that I can correct them. Lastly, this list should be considered "in-progress"; feel free to send me an email if you know of a book that should be included!

Title Author(s) License(s)
Abstract Algebra
Abstract algebra: Theory and applications Thomas W. Judson GFDLGNU Free Documentation License
Applied Math
Derivations of applied mathematics Thaddeus H. Black GPLv2GNU General Public License, version 2
Discrete Math
Applied combinatorics Mitchel T. Keller and William T. Trotter CC BY-SA 4.0Creative Commons Attribution-ShareAlike 4.0 International
Discrete mathematics: An open introduction Oscar Levin CC BY-SA 4.0Creative Commons Attribution-ShareAlike 4.0 International
Linear Algebra
A first course in linear algebra Robert A. Beezer GFDLGNU Free Documentation License
Linear algebra Jim Hefferon GFDLGNU Free Documentation License or CC BY-SA 2.5Creative Commons Attribution-ShareAlike 2.5 Generic
Linear algebra done wrong Sergei Treil CC BY-NC-ND 3.0Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported
Linear algebra via exterior products Sergei Winitzki GFDLGNU Free Documentation License
An infinite descent into pure mathematics Clive Newstead CC BY-SA 4.0Creative Commons Attribution-ShareAlike 4.0 International
Book of proof Richard Hammack CC BY-NC-ND 4.0Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International
Everything you always wanted to know about mathematics Brendan W. Sullivan ©

Reasoning behind this list

"The impact of open educational resources on various student success metrics" discusses the results of a large-scale study on the relationship between open-access educational resources and student success in the classroom. The study finds that the implementation of open-access resources improves student performance across a broad range of socio-economic breakdowns. This alone is motivation enough to strive to use as many open-access materials in the classroom as possible and is my main motivation behind keeping this list of textbooks.

I additionally subscribe to the free and open-source philosophy in general, especially in academics. Sergei Winitzki includes an excellent justification behind publishing his linear algebra book under a copyleft license (read the "Terms and conditions for distribution" section here).