The book gives an idea of both the current state of the basic sections of management theory, as well as some of its new and latest achievements. The basics of the state space method for linear dynamical systems and its application to the problems of nonlinear and adaptive control, including the control of oscillatory and chaotic processes, are considered. Methods of transformation of dynamic models and information on computational methods of systems analysis. The basics of the synthesis of observers and modal control. From the point of view of the state space method, properties and methods of studying nonlinear systems, including variable-structure systems and adaptive systems based on the bypass method, were considered. The presentation is accompanied by examples and exercises in the MATLAB language, widely used for scientific and engineering calculations in leading foreign and domestic universities. Designed for teachers, students and graduate students, as well as engineers and researchers interested in the analysis and synthesis of dynamic systems in specialties related to automation and management