Merging algebra and analysis, this text uses Lie-theoretic methods
to develop a theory with wide applications in mathematics and
physics. It aims to encourage the reader's understanding of Lie
theory to evolve from beginner to expert. Topics include: the
Cartan theory of complex semisimple Lie algebras; the Cartan-Weyl
theory of the structure of representations of compact Lie groups;
the classification of real semisimple Lie algebras; the structure
theory of noncompact reductive Lie groups; and integration on
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