Peter Smereka University of Michigan The purpose of my two lectures will be to first physically motivate simplified kinetic Monte Carlo models based on bond counting. These sorts of models are commonly used in the physics and engineering literature to gain insight into epitaxial growth especially in systems where atomistic effects are important. The implementation of bond counting KMC models will then described. Some physical and mathematical properties of this model will be outlined for the case of film undergoing relaxation (surface diffusion) in 1+1 dimensions. In particular, we will examine this model from the view point of statistical mechanics and as a continuous time Markov chain. The continuum limit of the model will be discussed. If time permits the incorporation of strain will be discussed.