In the past few years, new and deep methods in geometry have produced a remarkable insight on various aspects of representation theory of reductive groups : representations of semisimple Lie algebras and the theory of primitive ideals in their enveloping algebra, representations of finite groups of Lie type, representations of real and p-adic Lie groups, representations of adelic groups and representations of Hecke-algebras. These three volumes are the proceedings of a special period held on these questions in June and July of 1987 at Universite Paris 7, Universite de Paris-sud and Centre International de Rencontres Mathematiques in Marseille-Luminy. Some of the first synthetic presentations, by the best experts in the field, are given here, along with relevent research articles. This first volume is devoted more particularly to finite groups of Lie type.