Representation theory is the study of concrete realizations of the axiomatic systems of abstract algebra. It originated in the study of permutation groups, and algebras of matrices. The theory of group representations was developed in an astonishingly complete and useful form by Frobenius in the last two decades of the nineteenth century. Both Frobenius and Burnside realized that group representations were sure to play an important part in the theory of abstract finite groups. The first book to give a systematic account