Abstract

The first version of these notes was written for a first-year graduate algebra course. As in most such courses, the notes concentrated on abstract groups and, in particular, on finite groups. However, it is not as abstract groups that most mathematicians encounter groups, but rather as algebraic groups, topological groups, or Lie groups, and it is not just the groups themselves that are of interest, but also their linear representations. It is my intention (one day) to expand the notes to take account of this, and to produce a volume that, while still modest in size (c200 pages), will provide a more comprehensive introduction to group theory for beginning graduate students in mathematics, physics, and related fields. Please send comments and corrections to me at math0 at jmilne.org. v2.01 (August 21, 1996). First version on the web; 57 pages. v2.11 (August 29,2003). Fixed many minor errors; numbering unchanged; 85 pages.

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