Textbook in PDF format

From rings to modules to groups to fields, this undergraduate introduction to abstract algebra follows an unconventional path. The text emphasizes a modern perspective on the subject, with gentle mentions of the unifying categorical principles underlying the various constructions and the role of universal properties. A key feature is the treatment of modules, including a proof of the classification theorem for finitely generated modules over Euclidean domains. Noetherian modules and some of the language of exact complexes are introduced. In addition, standard topics - such as the Chinese Remainder Theorem, the Gauss Lemma, the Sylow Theorems, simplicity of alternating groups, standard results on field extensions, and the Fundamental Theorem of Galois Theory - are all treated in detail. Students will appreciate the text's conversational style, 400+ exercises, an appendix with complete solutions to around 150 of the main text problems, and an appendix with general background on basic logic and naïve set theory.
Treats all standard topics for a first course in detail, moving from rings to modules to groups to fields, which allows for a more gradual entry into the subject
Emphasizes a modern perspective, with hints toward category theory, exposing students to advanced topics and preparing them for graduate courses and applications of algebra in other subjects
Includes 400+ exercises, with 150 worked-out problems from the main text, and plenty of examples to help students better understand the material
Uses a conversational style and strong narrative flow that makes the material easier for students to follow and appreciate as a whole