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. Computational field theory and pattern formation.- Simulating granular media on the computer.- Some physical and computational aspects of self-organized criticality.- Critical percolation with moving disks.- Fourier techniques in numerical methods for evolutionary problems.- A fast algorithm for the generation of random numbers with exponential and normal distributions.- Numerical simulations of a nonlinear Klein-Gordon model. Applications.- Topics on chaotic dynamics.- Multistable steady states and oscillations in a suface reaction model.- Comparation of two Fokker-Planck modelings for a master equation.- Computational studies of the complex Ginzburg-Landau equation and its non-equilibrium potential.- Deterministic simulation of domain pattern formation under instantaneous nucleation conditions.- Morphological instabilities of a nematic-smectic B interface.- Dynamic time rescaled Monte Carlo algorithm.- Pattern formation in convection of rotating fluids.- Codimension two bifurcation in unidimensional heating.- Cylinders and wheels rolling into Chaos.- On the transition to columnar convection.- Finite temperature dc conductance of random dimer superlattices.- A multigrid approach to parallel simulations in nonlinear optics.- Surface electromagnetic waves on index-matched interfaces.- Conservative numerical schemes for Euler-Lagrange equations.- Suppression of chaotic behaviour in models of chemical chaos.- Perturbing variables in poincaré sections to suppress chaos.- Ergodic theory for unidimensional Jacobi Matrices.- Order in binary sequences and the properties of the routes to chaos.