The physics of surface and interface is an increasingly important area in the field of condensed matter physics. This book provides a comprehensive introduction to the kinetic Monte Carlo simulation for the submonolayer crystal growth phenomenon. The growth from vapor is studied under the condition meet in molecular beam epitaxy (MBE). It describes the basic physical processes, such as atomic process during growth, formulation of growth models, and surface diffusion and nucleation theory. It covers the effect of small-cluster mobility and adatom detachment on the island formation during the submonolayer epitaxial growth of the thin films deposition under the various conditions. This book may be useful for the undergraduates, graduate students and researchers in the field of surface and interface physics.