The contents of this volume of Astérisque are the results obtained and presented in the KGB Seminar at Rennes during the academie year 1971-1972. Except for the first expository lecture, which we have included for reference purposes, the proofs and a large part of the theorems are original contributions and published here for the first time. The basic theme is recurrence, renewal and normality of random walks on locally compact groups, with emphasis on the non-abelian case. Several related topics are also treated (e.g. contributions 6, 7 and 8). The results we have obtained are not complete, research con-tinues, and the organizers hope that this collection will stimulate further investigation.