Mathematics Textbooks for Self Study -- A Guide for the Autodidact



This is a list of suggested textbooks that a student can use to learn about a topic on their own, or to supplement the text used in a class.

This list is not meant to be comprehensive. It only contains popular topics encountered in undergraduate and the first year or two of graduate study. So, if you want book recommendations for something advanced (such as C*-algebra theory or Homological Algebra), or something specific (such as Knot theory or Coding theory), you will need to look elsewhere. I have also listed some of the best books for learning a topic, with no effort to list all the introductory texts on that topic. (But, if you think something missing from the list should be there, just let me know.)

Under each topic I have listed some of the books I've found most useful, as well as others that are likely to be on the recommendation lists of most mathematicians.



KEY

Books in Blue = Highly recommend (by me) as a first exposure to the topic.

Books in Green = Elementary, accessible with little background.

Books in Red = Difficult to read, but considered a standard and worthwhile if you can follow it.

Books in Purple = Older and considered a classic; may be difficult to read due to antiquated notation or terminology, but also contains useful material not found in newer books.

Books labeled (DOVER) are published by Dover Publications, also known as Dover Books, which primarily publishes reissues; i.e., books no longer published by their original publishers that are often, but not always, in the public domain. Dover books are very inexpensive, often in the range of $10--$20.




Abstract Algebra

Undergraduate
Graduate


Real Analysis

Undergraduate
Graduate


Complex Analysis

Undergraduate
Graduate


Functional Analysis



Ordinary Differential Equations (ODEs)

Undergraduate


Partial Differential Equations (PDEs)

Undergraduate
Graduate


Linear Algebra

Undergraduate
Graduate


Point-Set Topology

Advanced Undergraduate / Beginning Graduate


Algebraic Topology

Graduate


Differential Topology

Undergraduate
Graduate


Riemannian Geometry

Undergraduate
Graduate


Number Theory

Elementary Number Theory
Algebraic Number Theory
Analytic Number Theory
Elliptic Curves


Algebraic Geometry

Undergraduate
Graduate


Logic, Set Theory, and Computability

Undergraduate
Graduate


Category Theory