Discrete Contact Mechanics with Applications in Tribology presents new solutions to contact problems for elastic and viscoelastic bodies in normal, sliding, and rolling contact, taking into account effects such as surface microgeometry, adhesion, fluid films, and viscous hysteresis in bulk material or surface layers. These solutions are applied to problems in tribology for modeling contact and friction of bodies with surface microgeometry (rough or textured). The book provides exact mathematical formulations for cases of discrete contact based on classical approaches of contact mechanics, allowing readers to study the influence of different parameters of surface microgeometry on contact characteristics and friction force. The book will help solve problems in modeling contact and friction interaction in cases of discrete character of contact interaction, mutual influence of individual contact spots in contact interaction of elastic and viscoelastic solids, calculating sliding and rolling friction forces as a result of adhesive and viscoelastic mechanisms of dissipation, and more.