This book is devoted to the sndy of some clifferentia.l inclusions motivated by Mechanics and of existcnce rcsults for the dynamics of systems with inelastic shocks, with or without friction. This ensures a certain unity of subject, techniques and applications, at the price of not including some earlier works Mon 1-4] . In the introductory Chapter 0, sevcral essentia.l mathematical tools (either recent or recently rediscoven d) are presented. l1ainly they concern functions of bouncled variation defincd in real interva.ls ( deriva.tion of Stieltjcs measures, compactness results. convergencrc...