This manual pertains to the classic monograph "Groups, Rings, Modules" by Maurice Auslander and David Buchsbaum, published by Dover Publications. This comprehensive text is designed for advanced undergraduates and graduate students, presupposing a foundational understanding of sets, groups, rings, and vector spaces. The monograph is structured into four distinct parts, systematically exploring fundamental concepts in abstract algebra.

The manual provides detailed coverage of the book's content, including examinations of sets and maps, monoids and groups, categories, and rings in the initial section. Subsequent parts delve into unique factorization domains, general module theory, semisimple and Artinian rings, localization, tensor products, principal ideal domains, algebraic field extensions, and Dedekind domains. Exercises are included at the end of each chapter, facilitating a deeper engagement with the material for students and researchers in abstract algebra.