I. Martin Isaacs, University of Wisconsin, Madison, WI.

• Part One. Noncommutative algebraChapter 1. Definitions and examples of groupsChapter 2. Subgroups and cosetsChapter 3. HomomorphismsChapter 4. Group actionsChapter 5. The Sylow theorems and $p$-groupsChapter 6. Permutation groupsChapter 7. New groups from oldChapter 8. Solvable and nilpotent groupsChapter 9. TransferChapter 10. Operator groups and unique decompositionsChapter 11. Module theory without ringsChapter 12. Rings, ideals, and modulesChapter 13. Simple modules and primitive ringsChapter 14. Artinian rings and projective modulesChapter 15. An introduction to character theoryPart Two. Commutative algebraChapter 16. Polynomial rings, PIDs, and UFDsChapter 17. Field extensionsChapter 18. Galois theoryChapter 19. Separability and inseparabilityChapter 20. Cyclotomy and geometric constructionsChapter 21. Finite fieldsChapter 22. Roots, radicals, and real numbersChapter 23. Norms, traces, and discriminantsChapter 24. Transcendental extensionsChapter 25. the Artin-Schreier theoremChapter 26. Ideal theoryChapter 27. Noetherian ringsChapter 28. IntegralityChapter 29. Dedekind domainsChapter 30. Algebraic sets and the Nullstellensatz

Unlike similar textbooks, this volume steers away from chapter-end problems by including full details of all proofs as problems are presented."" - SciTech Book News""This is a book to be warmly welcomed. The presentation throughout is a model of clarity, and the proofs are precise and complete. The careful reader will learn (much) from it, not only mathematics, but also (and more importantly) how to think mathematically."" - Mathematical Reviews""Isaacs' Algebra, A Graduate Course is a pedagogically important book, to be highly recommended to fledgling algebraists-and every one else, for that matter."" - MAA Reviews""Most of these extra topics are not usually covered in first-year graduate algebra courses, or in introductory textbooks on modern algebra, but here they are woven into the main text in very natural, effective and instructive a manner, thereby offering a wider panorama of abstract algebra to the interested reader. This profound algebra text will prepare any zealous reader for further steps into one or more of the many branches of algebra, algebraic number theory, or algebraic geometry. Also, it will maintain its well-established role as one of the excellent standard texts on the subject, as a highly recommendable source for instructors, and as an utmost valuable companion to the various other great textbooks in the field."" - Zentralblatt MATH