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Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Compact groups. --- Locally compact groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Compact groups --- Topological groups --- Groups, Compact --- Locally compact groups

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Algebras, Linear --- Representations of groups --- 512 --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algebra --- Algebras, Linear. --- Representations of groups. --- 512 Algebra --- Algèbre linéaire --- Algèbre multilinéaire. --- Multilinear algebra --- Algèbre tensorielle. --- Tensor algebra --- Algèbre extérieure --- Algèbre linéaire --- Représentations de groupes --- Representation des groupes