Representation theory of compact groups

Group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well-understood. The present thesis consists of three chapters. First chapter is about the topological groups and some related results. In the second chapter we have studied the Haar measure on locally compact groups and finally the third chapter contains the representation theory of compact groups and Peter-Weyl theorem.