The volume is dedicated to A.A. Kirillov and emerged from an international conference which was held in Luminy, Marseille, in December 2000, on the occasion of Alexandra Alexandrovitch's 26th birthday. The conference was devoted to the orbit method in representation theory, an important subject that influenced the development of mathematics in the second half of the XXth century. Among the famous names related to this branch of mathematics, the name of A.A. Kirillov certainly holds a distinguished place, as the inventor and founder of the orbit method.