Knowledge of group theory and linear algebra. Notions of Galois theory and differential geometry.
The aim of representation theory is to determine all possible symmetry operations of a given group. For a finite group this info is contained in the character table. We prove the main results such as complete reducibility, orthogonality relations and Frobenius reciprocity. We learn to deduce group theoretic infoirmation from the character table, for example to determine all normal subgroups of the group.