Contains articles by many of the participants at the conference on modular representation theory of finite groups, which took place under the auspices of the Mathematical Research Institute of the Ohio State University with additional support from the National Science Foundation. The book is addressed to specialists and students in the field of group representation theory, including both the general theory and the special theories related to the representations of the symmetric groups and the finite groups of Lie type. Latest reports are given on important conjectures including the Lusztig conjecture, the Alperin-McKay-Dade conjectures and the k(GV) problem. Important new research avenues are illuminated, including the theory of infinite-dimensional modules for finite groups and the theory of Rickard equivalences of module categories.