This monograph contains the main results of research in the field of constructing mathematical models of nature and society, obtained by the Institute of Mathematical Modeling of the Russian Academy of Sciences in collaboration with the GUIS FAPSI and the sociological faculty of Moscow State University . M. In. Lomonosov . These studies focus on the problems of mathematical modeling of the development of complex situations arising in nature and society. With the help of monitoring and modeling decision support systems, it is possible to find the best ways and means to get out of emergencies . The results obtained in the works included in this monograph are currently actively used in scientific research and in decision-making by the management structures of society. The monograph will be useful for researchers and managerial personnel, as well as for all students and mastering knowledge in this field of mathematical modeling.