Collection of works on mathematical theory of systems, written by leading foreign experts I. Willems, A. van der Shaft (Netherlands), U. Helmke (Germany), B. Wymen (USA) et al. They develop the theory of the implementation of Kalman for a wide class of systems (the famous problem of the black box), indicate its practical use; the topological structure of the space of modules of systems is studied; the relationship between local and global theory of linear systems is studied. The book uses a modern mathematical apparatus, but almost all the material is designed for the reader who first gets acquainted with such methods of studying systems. For mathematicians interested in systems theory, specialists in mathematical modeling and management of complex objects, graduate students and university students .