The evolution of human communication with computers is associated with the creation of powerful tools for their mathematical support. The developed languages and programming systems used in this case significantly increase the "Intelligence" of the computer, implemented both in a schematic and program way, and contribute to the further expansion of the scope of application of computer technology. The solution of the problems arising in this connection caused the formation and development of theoretical programming and the penetration into it of the ideas and methods of general algebra. The monograph is devoted to the study of algebraic methods, taking into account their application in theoretical and system programming: applied theory of algorithms, theory of formal languages and programming systems.