This is a modern presentation of the theory of representations of locally compact groups. In a small number of pages, the reader can get some of the most important theorems on this subject. Many examples are provided.

Highlights of the volume include:

(1) A generous introduction explaining the origins of group theory and their representations, the motivation for the main problems in this theory, and the deep connections with modern physics.
(2) A solid presentation of the theory of topological groups and of Lie groups.
(3) Two proofs of the existence of Haar measures.
(4) The detailed study of continuous representations on general locally convex spaces, with an emphasis on unitary representations of compact groups on Hilbert spaces.
(5) A careful presentation of induced representations on locally convex spaces and G. W. Mackey's Theorem of Imprimitivity.



About half of the results included in this volume appear for the first time in a book, while the theory of $p$-induced representations on locally convex spaces is new. To facilitate reading, several appendices present the concepts and basic results from general topology, differential manifolds, abstract measures and integration, topological vector spaces, Banach spaces, Banach algebras, $C^*$-algebras, and operator theory on Hilbert spaces.