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The interest in the problem of surface diffusion has been steadily growing over the last fifteen years. This is clearly evident from the increase in the number of papers dealing with the problem, the development of new experimental techniques, and the specialized sessions focusing on diffusion in national and international meetings. Part of the driving force behind this increasing activity is our recently acquired ability to observe and possibly control atomic scale phenomena. It is now possible to look selectively at individual atomistic processes and to determine their relative importance during growth and reactions at surfaces. The number of researchers interested in this problem also has been growing steadily which generates the need for a good reference source to farniliarize newcomers to the problem. While the recent emphasis is on the role of diffusion during growth, there is also continuing progress on the more traditional aspects of the problem describing mass transport in an ensemble of particles. Such a description is based on the statistical mechanical analysis of a collection of particles that mutually interact and develop correlations. An average over the multitude of atomistic processes that operate under these conditions is necessary to fully describe the dynamics in the system.