This significantly enlarged and expanded second edition, focuses on a class of nonsmooth hybrid dynamical systems, namely finite dimensional mechanical systems subject to unilateral constraints. It contains a complete overview of the main problems in the areas of mathematics, mechanics, stability and control, which are of interest in this field. The following topics are discussed in detail and are illustrated with examples : shock dynamics, multiple impacts, feedback control, Moreau's sweeping process, complementarity formulations. With a comprehensive bibliography of over a thousand references, this book is an indispensable source of information on the subject treated. The Communications and Control Engineering Series reflects the major technological advances which have a great impact in the fields of communication and control. It reports on the research in industrial and academic institutions around the word to exploit the new possibilities which are becoming available.