Title: Introduction to the theory of generalized solutions of Hamilton-Jacobi equations.

Annotation: The course of lectures will focus on Hamilton-Jacobi equations, which are first-order nonlinear partial differential equations. The first lecture will be devoted to the origin of Hamilton-Jacobi equations in optimal control problems and differential games. The second lecture will cover the basics of the theory of minimax (generalized) solutions to Cauchy problems for Hamilton-Jacobi equations. In the third lecture, viscosity (generalized) solutions to such problems will be considered.