Linear groups and linear representations; Lie groups and Lie algebras; orbital geometry of the adjoint action; coxeter groups, Weyl reduction and Weyl formulas; structural theory of compact Lie algebras and compact connected Lie groups.

An introduction to the theory of compact connected Lie groups and their representations, and a presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a balance between the algebraic and geometric aspects of Lie theory.