Advanced Calculus

Written by Lynn H. Loomis and Shlomo Sternberg from the Department of Mathematics at Harvard University, this huge online calculus textbook is available in PDF form. (It is 592 pages and over 57 MB.) This revised edition was published in 1990 and is based on an honors course in advanced calculus. The authors suggest using the text as a year-long course in advanced calculus or as a three-semester long introduction to analysis. Students should be familiar with calculus, linear algebra and partial derivatives prior to attempting this course. The first half of the textbook develops calculus with a strong focus on differential calculus in the setting of normed vector spaces and the second half of the book deals with the calculus of differentiable manifolds.

A First Book in Algebra

Wallace C. Boyden, 1895. This algebra textbook explains concepts well and might make a good reference source. It has many great practice problems but without an answer key, this vintage math textbook might not be a good choice for self-study.