An excellent series of textbooks covering the secondary school mathematics curriculum is produced by Art of Problem Solving. For books that go beyond the standard secondary school curriculum, see below.

 

Foundations

• R. Hammack, Book of Proof (3rd Ed.)

• K. Houston, How to Think Like A Mathematician.

 

Calculus

• J. Stewart, Calculus (9th Ed.)

• M. Spivak, Calculus (4th Ed.)

 

Abstract Algebra

• J. Beachy & W. Blair, Abstract Algebra (4th Ed.)

 

Linear Algebra

• H. Anton & C. Rorres, Elementary Linear Algebra (11th Ed.)

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Probability

• J. Hwang & J. Blitzstein, Introduction to Probability (2nd Ed.)