From the reviews of the second edition:

“This book certainly has more than enough material for a two-semester algebra course for first-year graduate students. … The balance among various topics will please some instructors more than others.” (Miklós Bóna, MathDL, September, 2007)

“The book under review is the second edition of the author’s sweeping text originally titled ‘Algebra’ … . All together, the second edition of P. A. Grillet’s standard primer is a masterly, clearly written, comprehensive and self-contained algebra text for graduate students, with a plentiful supply of additional advanced material … . Moreover, the book under review, in its didactically oriented disposition, represents an excellent source for teachers and instructors of graduate courses in abstract algebra as well.” (Werner Kleinert, Zentralblatt MATH, Vol. 1122 (24), 2007)

“Abstract Algebra” is a clearly written, self-contained basic algebra text for graduate students, with a generous amount of additional material that suggests the scope of contemporary algebra. The first chapters blend standard contents with a careful introduction to proofs with arrows. The last chapters, on universal algebras and categories, including tripleability, give valuable general views of algebra. There are over 1400 exercises, at varying degrees of difficulty.

For the new edition, the author has completely rewritten the entire text, streamlining the first chapters for rapid access to Galois theory, removing some material, and adding introductions to Groebner bases, Ext and Tor, and other topics.

From a review of the First Edition:

…combines an exceptionally accessible discussion of the basic material with a just as thorough and well-organized treatment of the many additional (advanced) topics included…. represents an outstanding introduction to modern abstract algebra as a whole, with many unique features. It captivates the reader by its remarkable diversity, comprehensiveness, elegant succinctness, and coherence.

– Werner Kleinert, Zentralblatt

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