The "Monte Carlo method" is a method of computer simulation of a system with many degrees of freedom, and thus it has widespread applications in science. It takes its name from the use of random numbers to simulate statistical fluctuations in order to numerically gen- erate probability distributions (which cannot otherwise be known explicitly, since the systems considered are so complex). The Monte Carlo method then yields numerically exact information on "model systems". Such simulations serve two purposes: one can check the extent to which a model system approximates a real system; or one may check the validity of approximations made in analytical theories. This book summarizes recent progress obtained in the implementation of this method and with the general analysis of results, and gives concise reviews of recent applications. These applications include simulations of growth processes far from equilibrium, interfacial phenomena, quantum and classical fluids, polymers, quantum problems on lattices, and random systems.