This book discusses the general patterns of evolution of the World System. It is shown that they can be described using extremely simple mathematical models. The relationship between micro-level chaos and highly deterministic dynamics at the macro level is considered. The relationship between cyclic and progressive processes is analyzed. The analyzed data and developed models make it possible to propose a number of specific recommendations, in particular, to identify ways to solve the demographic crisis in Russia. The book offers fundamentally new sections on the factors of investment activity, forecasting the dynamics of political instability and the demographic future of Russia, as well as sections devoted to system analysis and mathematical modeling of the interaction between the center and the periphery of the World System. The monograph widely uses the method of mathematical modeling. At the same time, the book contains the necessary explanations that make it accessible to a mathematically unprepared reader. At the most popular level, the basic mathematical methods used in the humanities are explained to the reader using specific examples. The book is intended for a wide range of readers interested in the history of human civilization, patterns of world development and problems of integration of exact, natural and social sciences.