This is an elementary introduction to the representation theory of
real and complex matrix groups. The text is written for students in
mathematics and physics who have a good knowledge of
differential/integral calculus and linear algebra and are familiar
with basic facts from algebra, number theory and complex analysis.
The goal is to present the fundamental concepts of representation
theory, to describe the connection between them, and to explain
some of their background. The focus is on groups which are of
particular interest for applications in physics and number theory
(e.g. Gell-Mann's eightfold way and theta functions, automorphic
forms). The reader finds a large variety of examples which are
presented in detail and from different points of view.
General
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