This book contains review articles and original results in problems and methods of mathematical simulation and their applications in various fields. The articles included are based on the reports that were presented at the Fourth International Mathematical Modeling Conference (Moscow, Russia, June 27 - July 1, 2000). The book is intended for specialists, as well as for post-graduates and students in the areas of mathematical modeling, algorithms and computational theory, mathematical physics, discrete mathematics, physics, physical chemistry, transfer theory, and economics.