Abstract algebra: theory and applications - Thomas Judson

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Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner.

Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications.

The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course.

The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.