In the textbook, along with the presentation of the principles of classical variational calculus, the basics of direct methods and elements of the theory of discontinuous variational problems are considered. Some attention in the manual is paid to the scientific results of the Nizhny Novgorod School of Variational Calculus . In addition to the presentation of the foundations of the theory, the manual contains examples of solving variational problems, including with the use of the MATLAB system; problems for independent solution are given The electronic teaching aid is intended for UNN students studying in the direction of training 080500 "Business Informatics", studying the course "Methods of optimization" .