This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction and a major part of the analysis of dynamic contact problems without friction. Much of this work emerged from the authors' research activities over the past 10 years and deals with an approach proven fruitful in many situations. They pay careful attention to quantification and precise results to get optimal bounds in sufficient conditions for existence theorems. Self-contained and up to date, this is a complete collection of the available results and techniques for the analysis of unilateral contact problems and builds the background required for further research.