The basic concepts and definitions of the mathematical theory of optimal control processes. are considered. The main methods of the theory of optimal processes are analyzed, the main problems of optimal control are set, the necessary conditions of optimal control and the mathematical apparatus that allows to obtain solutions for different classes of problems. Dop. Information: Academic Council of TSTU recommended for students of higher education institutions , students in the specialties 230201 "Information Systems and Technologies" , 090105 "Integrated information security of automated systems" , and for students of secondary vocational education, students in specialty 230105 "Software of computer equipment and automated systems" .