Friction is an old and important but at the same time very complex physical event. This thesis aims to develop an atomic scale theory of friction. VVe investigate various atomic processes and stick-slip motion by using simple models and by using simulation of realistic systems based on the stateof-the art molecular dynamics and ab-initio electronic structure and force calculations. Theoretical studies of dry sliding friction, which has a close l)earing· on the experiments done by using the atomic and friction force microscope were performed. First, a simple model is used to investigate the basic mechanisms of friction and stick-slip motion, whereby the effect of material parameters and local elastic deformation of the substrate were also examined. Then, atomic scale study of contact, indentation, subsequent |)ulling and dry sliding of a sharp and blunt metal tips on a metal surface were studied. In order to understand the atomic-scale aspects of boundary lubrication such as interesting covera.ge and load dependent behavior and structural transformations, molecular dynamics simulations were performed on a model system that has two .'i(110) surfaces and a. xenon layer confined between these two surfaces. Finally, in view of the atomic processes revealed from computer simulations an energy dissipation mechanism and quantum heat conduction were studied.