# Topics - Definitions, motivations, and basic structure theory. - Root systems, Weyl groups, the finite simple Lie algebras. - Theorems of Engel and Lie (on solvability), Cartan (on Killing forms), Weyl (on complete reducibility). - The classification of simple complex Lie algebras - Classification of finite-dimensional representations, Verma modules, the combinatorics of characters. - Crystal bases.