This volume contains extended versions of the five plenary lectures given at the Euromech Colloquium 397 "Impact in Mechanical Systems", at Grenoble, from June 30 until July 1-2, 1999, France. As the title indicates, it is devoted to the study of rigid multi-body mechanical systems subject to nonsmooth effects, such as impacts, Coulomb friction, constraints addition and deletion. Actually, this represents a large and important class of nonsmooth mechanical systems. Its study can be traced back to the ancient Greeks. The 17th and 18th centuries also witnessed a great deal of (scientific) excitement about shock dynamics. Prestigious names like Descartes, Newton, Poisson, Gauss, Huygens, Bernoulli, to name a few, have long been attached to the study of collisional effects between two rigid bodies.