The monograph is devoted to the discussion of modern approaches to mathematical modeling of reflection. The authors introduce a new class of theoretical and game models - reflexive games describing the interaction of subjects (agents) making decisions on the basis of a hierarchy of ideas about significant parameters, ideas about representations, etc. d. Analysis of the behavior of phantom agents , existing in representations of other real or phantom agents , Properties of Information Structure , Reflecting the mutual awareness of real and phantom agents , allows us to offer an information equilibrium as a solution to the reflexive game , which is a generalization of a number of well-known equilibrium concepts in non-cooperative games. Reflexive games make it possible to model the behavior of reflective subjects , explore the dependence of agents' winnings on their reflection ranks, Set and solve tasks of reflexive management , uniformly describe many phenomena, Reflection-related (hidden control, Information Management through the Media , Reflection in Psychology , Artistic works and others. ). The book is addressed to specialists in the field of mathematical modeling and management of socio-economic systems, as well as university students and graduate students .