This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: mathematical and computer discrete systems models; non-linear excitation in condensed media; complex systems evolution; mathematical models in economics; non-equilibrium processes...