Linear Representations of Groups

This chapter discusses the theory of linear representations of finite groups in detail. It offers a succinct review of a well-known theory that helps readers without previous knowledge to grasp the main ideas and to put it to use immediately. The chapter presents a smooth transition from the standard presentations of the theory of linear representations to the language that helps very much in developing the theory of representations for groupoids. It addresses the notions of linear representations of groups, their equivalence and the main questions regarding their structure. The notion of unitary representations, with the corresponding background of Hilbert spaces (finite-dimensional mostly) are discussed. The chapter also presents the statement of Schur’s lemmas.