This volume gives a general outline of the various activities which took place during the research semester Group Representation Theory, held in Lausanne, Switzerland, from January to June, 2005. There are contributions by : J.F. Carlson, R. Kessar, M. Linckelmann, J. Thévenaz, P. Webb, M. Broué, S. Donkin, M. Geck, G. Seitz, J.-P. Serre.