Groups and representations

the long version

This book provides a concise treatment of some topics from group theory and representation theory, suitable for a one-term course. It focuses on the non-commutative side of the field, emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as advanced undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.