TITLE: Good book on representation theory after reading Rotman
QUESTION [8 upvotes]: I'm about to finish Rotman's "Introduction to the Theory of Groups" and I would like to continue my study of group theory with a book on representation theory. The book should give a broad overview over the different areas of representation theory. It may assume the reader to be familiar with the basic theory of groups. I like Rotman's system of offering a large amount of excersices some of which are used in latter sections of the book.

REPLY [6 votes]: I would recommend the books of I.M. Isaacs Character Theory of Finite Groups (1976) and J.P. Serre Linear Representations of Finite Groups (1977). Both excellent books written by the real masters and with plenty of exercises! Also the five (!) volumes of Gregory Karpilovsky on Group Representations are fantastic sources of knowledge. If you want to go into modular representation theory and projective representation theory, look for the books of Bertram Huppert or B. M. Puttaswamaiah, John D. Dixon, and again Karpilovsky respectively.