The book covers the basics and some generalizations of Monte Carlo methods and its applications to discrete and field theoretic models. It covers the study of nonequilibrium models of granular media by computer simulation and pattern formation. Furthermore, the lectures deal with details of phenomena such as chaos, segregation, pattern formation and phase transitions, convection, fluidification, density waves, surface reaction and growth, spread of epidemics, acoustics, deformation, etc. The book addresses students in physics and scientific computation. It should be a valuable reference work for researchers as well.