Knapp A. Basic Algebra 2ed 2016

Textbook in PDF format

In the years since publication of the first edition of Basic Algebra, many readers have reacted to the book by sending comments, suggestions, and corrections. People especially approved of the inclusion of some linear algebra before any group theory, and they liked the ideas of proceeding from the particular to the general and of giving examples of computational techniques right from the start. They appreciated the overall comprehensive nature of the book, associating this feature with the large number of problems that develop so many sidelights and applications of the theory.
Preliminaries about the integers, polynomials, and matrices
Vector spaces over q, r, and c
Inner-product spaces
Groups and group actions
Theory of a single linear transformation
Multilinear algebra
Advanced group theory
Advanced group theory (continued)
Commutative rings and their modules
Fields and galois theory
Modules over noncommutative rings
Appendixes
Sets and Functions
Equivalence Relations
Real Numbers
Complex Numbers
Partial Orderings and Zorn’s Lemma
Cardinality