Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title "Lie Theory," feature survey workand original results by well-established researchers in key areas of semisimple Lie theory.

A wide spectrum of topicsis treated, with emphasis onthe interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well asfor infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces,and harmonic analysis through a far-reaching generalization of Harish--Chandra'sPlancherel formula for semisimple Lie groups.

Idealfor graduate students and researchers, "Lie Theory" provides a broad, clearly focused examination of semisimple Lie groups and theirintegral importance to research inmany branches of mathematics.

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