This thesis is a theoretical study of atomic diffusion processes in condensed matter, with particular emphasis on surface diffusion. Oxygen adsorption and diffusion on the (111) surface of platinum is studied using a first-principles pseudopotential plane-wave approach based on density functional theory, with local (LDA) and semi-local functionals (GGA) for the exchange-correlation energy. The study resolves an inconsistency between experimental and theoretical results in the literature. The oxygen induced surface buckling and vibrational frequencies are found to be in good agreement with experimental data. This first-principles method is also used to explore the diffusion processes at edges, kinks, and corners of islands on the Al(111) surface. The calculated diffusion barriers are converted into a set of activation temperatures through ordinary transition state theory, and used to predict the temperature evolution of the surface morphology. Recent scanning tunneling microscopy experiments confirm several calculated results in great detail, which indicates a good accuracy in the theoretical approach. The Al(111) surface is further investigated in a first-principles study of the dynamics and diffusion of Al dimers. An unexpected ground state is found and explained in terms of elastic energy. A new diffusion path is revealed and shown to be blocked by compressive strain. A smooth potential energy surface enables exotic dynamic behavior, and the possibility of a pure metal quantum rotor is addressed.<p /> The time domain is stretched considerably in a kinetic Monte Carlo study on the motion of large atom islands. A fundamental break-down of regular scaling theory is found, which is now confirmed by experiments and other simulations. This result calls for a reevaluation of experimental analysis where the atomic migration mechanism has been deduced from the size scaling of the diffusion coefficient, and bears consequences in long-time studies of the evolution of the surface morphology by coarsening and Ostwald ripening. The shortcomings of scaling theory are addressed with the development of a new, kinetic, theory.<p /> Self-diffusion in liquid gold is studied using a many-atom interaction potential within the effective-medium theory. Thermal and structural properties are in good agreement with experimental results. The molecular dynamics simulations reveal a parabolic temperature dependence of the self-diffusion coefficient, as recently measured in micro-gravity experiments on other non-simple metals
