This monograph deals with certain aspects of the general theory of systems. The author develops the ergodic theory, which is the theory of quaslinvariant and invariant measures in such infinite-dimensional vector spaces which appear as models of various (physical, economic, genetic, linguistic, social, etc.) processes. The methods of ergodic theory are successful as applied to study properties of such systems. A foundation for ergodic theory was stimulated by the necessity of a consideration of statistic mechanic problems and was directly connected with the works of G. Birkhoff, Kryloff and Bogoliuboff, E. Hoph and other famous mathematicians.