The rapid development of various branches of the theory of optimal automatic systems made it timely to cover from some single point of view the main aspects of this theory. Such an attempt was made by the author in the chapter "Optimal Systems," which was included in the collection "Disciplines and techniques of Systems Control" edited by Dr. Pashon (Luxembourg), as well as in the course of lectures given in 196162 to graduate students and employees of the Institute of Automation and Telemechanics. The point of view presented there is also the basis of this book. She determined the sequence of presentation.