The monograph is devoted to methodological issues of constructing mathematical models of dynamic processes and phenomena of different nature. In the first part of the book, the simplest examples show how the formation of physical models took place from Aristotle to Einstein and what basic principles formed the basis of formation. The second part deals with models of automatic control systems, and their example shows how the methodology of physical and mathematical sciences penetrated into a new area - the design of controlled technical systems. The third part deals with mathematical models of systems in which a person plays a significant role - economic and social systems. The book explains what requirements are imposed on the results of > and in terms of penetration into the essence of the phenomenon under study, and from the point of view of the ershish of mathematical culture. For applied researchers using mathematical methods. It is also useful for mathematicians interested in new application areas.