Boundary value problems involving contact are important for industrial applications in both mechanical and civil engineering, such as structural foundations, bearings, metal forming processes, rubber sealings, drilling problems, crash analysis of cars, rolling contact between car tyres and the road, cooling of electronic devices, and many more. Other applications are related to biomechanical engineering design, where human joints, implants or teeth are considered. Due to this variety, contact problems today are combined either with large elastic or inelastic deformations, including time-dependent responses. Thermal coupling may also have to be considered, and even stability behaviour has to be linked to contact, such as wrinkling arising in metal forming problems. The topic of computational contact is described in depth here, providing differen formulations, algorithms and discretisation techniques for contact problems that have been established in the geometrically linear and nonlinear ranges. This book provides thé necessary continuum mechanics background. Special geometrical relations needed to se up the contact constraints are derived, and constitutive equations stemming from tribolog ; which are valid at the contact interface are discussed in detail, without going into numerical treatment. Solid and beam contact is considered, as is contact of unstable systems and thermomechanical contact. The algorithmic aspects touer a broad range of solution methods. Additionally, adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations.