This book proposes one of the possible approaches to solving problems of modeling large social systems. First, the issues that needs to be considered when developing models are qualitatively described. In this regard, analogies of the behavior of large social systems with artificial neural networks are indicated. Some issues of the mental properties of an individual are given, which should be taken into account when building models. One of the main among them is taking into account the internal image of the external world in the representation of the individual. Consideration of the inner image allowed proposing new ways to consider other common problems - for example, the archetypes in consciousness. Consideration of the issues indicated above made it possible to propose appropriate mathematical models that allowed, for example, describing some aspects of the problem of sustainable development. Some issues of anticipation in to public systems are considered. The book also contains mathematical models of both large social systems and some mental processes of individuals. In some cases, illustrations of the application of the proposed models are given: to geopolitics, the stock market, the formation of public opinion.