A classic graduate textbook and reference, originally published as AlgFbres enveloppantes . Provides a systematic exposition of the algebraic approach to representations of Lie groups via representations of the corresponding universal enveloping algebras. Assumes a general knowledge of Lie groups, and outlines the specific aspects needed. The 1996 reprint updates the status of open problems and adds a couple pages of bibliographic references. Annotation c. by Book News, Inc., Portland, Or.