The fields of boundary integral equations and of inequality problems, or more gen­ erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these developments in that open problems have been attacked succesfully and entirely new methodologies have been developed. The contact problems of elasticity is a class of problems which has offered many open questions to deal with, both to the research workers working on the theory of boundary integral equations and to those working on the theory of inequality problems. Indeed, the area of static and dynamic contact problems could be considered as the testing workbench of the new developments in both the inequality problems and in the boundary integral equations. This book is a first attempt to formulate and study the boundary integral equations arising in inequality contact problems. The present book is a result of more than two decades of research and teaching activity of the first author on boundary integral equations and, of the second author, on inequality problems, as well as the outgrowth of seminars and courses for a variety of audiences in the Technical University of Aachen, the Aristotle University of Thessa­ loniki, the Universities of Bochum, of Hamburg and Braunschweig, the Pontificia Univ. Catolica in Rio de Janeiro etc.