A method is presented to measure both the barriers for intra-and interlayer diffusion for an epitaxial system with great accuracy. It is based upon the application of mean-field nucleation theory to variable temperature STM data. The validity and limits of applying nucleation theory to extract barriers for terrace diffusion are discussed in comparison to alternative methods like Kinetic Monte-Carlo (KMC) simulations. With this approach, a pronounced influence of strain on intra-and interlayer diffusion was established for Ag self diffusion on strained and unstrained Ag(lll) surfaces. The strained surface was the pseudomorphic Ag monolayer on Pt(lll) which is under 4.3% compressive strain. The barrier for terrace diffusion is observed to be substantially lower on the strained, compared to the unstrained Ag/Ag(lll) case, 60+/-10 meV and 97+/-10 meV, respectively. A general method for the quantitative determination of the additional barrier for descending at steps is presented. It is based on the measurement of the nucleation rate on top of previously prepared adlayer islands as a function of island size and temperature. Application of this method reveals a considerable effect of strain also on interlayer diffusion. The additional barrier for interlayer diffusion decreases from 120+/-15 meV for Ag(111)homoepitaxy to only 30+/-5 meV for diffusion from the strained Ag layer down to the Pt(lll) substrate. These examples illustrate the strong influence of strain on the intra-and interlayer mass transport which leads to a new concept of layer-dependent nucleation kinetics for heteroepitaxial systems. Finally, we discuss the relation between corner diffusion and island shapes. Low temperature aggregation on hexagonally close-packed metal surfaces generally is dominated by the microscopic difference between two edge orientations giving rise to anisotropic corner (and edge) diffusion. It is demonstrated how this anisotropy gives rise to dendritic island shapes with trigonal symmetry.