This small booklet offers a testimony to the origins of representation theory. It starts with an introduction by W. Ledermann followed with a curriculum by I. Schur. The reader will find copies of the invitation to I. Schur to lecture in Zürich and his answer, from 1936. The main body of the book consists of I. Schur’s lectures “Darstellungstheorie der Gruppen”, which were written up and published by E. Stiefel in 1936. The text starts with matrix calculus and an introduction to linear transformations and the concept of a group. In the first chapter, basic notions and methods of representation theory are introduced. The theory of representations of finite groups is presented in the second chapter. In the last chapter, the author develops the theory of characters for finite groups.