Lie algebras are essential to the understanding of Lie groups. On the other hand, Lie algebras are also an important topic in algebra.
In this course we will concentrate on the algebraic aspects of the theory. In the first part of the course we will study finite dimensional Lie algebras, the classification of simple Lie algebras and their finite dimensional representations. In the second part we will then consider infinite dimensional Lie algebras with a particular emphasis on Kac Moody algebras.