A representation of a group G is, informally, a collection of invertible linear transformations of some vector space over a field (or, more generally, of some module over a ring), which multiply according to the same multiplication table as G. In other words, it is the choice a set of symmetries of a vector space, which reflect the group structure of G.
As symmetry is one of the fundamental concepts of mathematics, representations of groups arise in many different areas of mathematics: number theory, topology, combinatorics, differential geometry, algebraic geometry, ....
In this seminar we will learn the foundations of the theory of representations of finite groups. After defining the basic notions, we will first study representations of groups on vector spaces over fields of characteristic 0. This leads to a beautiful and mostly complete theory, which is already very useful.
For further information please check the seminar website: http://www.mi.fu-berlin.de/users/kindler/teaching/representation-theory-ss17_de.html