  A brief introduction is given to Kinetic Monte Carlo (KMC) simulations of
epitaxial crystal growth. Molecular Beam Epitaxy (MBE) serves as the prototype
example for growth far from equilibrium. However, many of the aspects discussed
hear would carry over to other techniques as well. A variety of approaches to
the modeling and simulation of epitaxial growth has been applied. They range
from the detailed quantum mechanics treatment of microscopic processes to the
coarse grained picture in terms of stochastic differential equations or other
continuum approaches. Here, the focus is on discrete representations such as
lattice gas and Solid-On-Solid (SOS) models. The basic ideas of the
corresponding KMC methods are presented. Strengths and weaknesses become
apparent in the discussion of several levels of simplification that are
possible in this context.
