Symmetries, in a very general sense, are a central part of mathematics and its applications. For example they appear in the geometry of everyday objects, in art and architecture, and in classical, quantum, and particle physics. Within mathematics they touch every area, from differential equations to number theory.

This course will introduce the abstract notions of

* groups, Lie groups and Lie algebras* and focus on the study of their

*representation theory*. A variety of applications will be discussed.