References for Group Theory
The following are excellent sources for the indicated areas in Group Theory.

Foundations, MSC 20A

1. David S. Dummit, Richard M. Foote, Abstract Algebra, John Wiley and Sons, Inc. 1999
2. I. N. Herstein, Topics in Algebra, Xerox College Publishing, 1975.

   A classic undergraduate textbook introducing groups, rings, fields, and linear algebra.

3. Serge Lang, Algebra, Addison-Wesley Publishing Company, 1997.

   A textbook covering a broad range of topics in algebra; some emphasis is placed on the parts of algebra most useful in algebraic geometry. In particular, basic homological algebra and basic category theory are well covered.

4. John S. Rose, A Course on Group Theory, Dover Publications, New York, 1994.
5. Thomas W. Hungerford, Algebra, Springer-Verlag Graduate Texts in Mathematics 73, 1974.

   Covers all of algebra from a more classical viewpoint; when dealing with rings, the focus is on noncommutative rings. Only two chapters on group theory are present. A brief discussion of categories is included.

6. Joseph J. Rotman, An Introduction to the Theory of Groups, fourth edition, Springer-Verlag Graduate Texts in Mathematics 148, 1994.

   A thorough introduction to the theory of groups. Emphasis is on groups with no further structure; includes a chapter on computability issues and the word problem.