The aim of this monograph is to partially address this need by providing state-of-the-art mathematical modelling and analysis of some of the phenomena that take place when a deformable body comes into quasistatic contact. We present models for the processes, describe the mathematical results, and provide representative proofs. A comprehensive list of recent references supplements this work. Between the time we started writing this monograph and the present, W. Han and M. Sofonea published the book “Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,” which focuses on mathematical and numerical analysis of contact problems for viscoelastic and viscoplastic materials.