The material will be relatively self-contained and accessible to undergraduate sec- ond and third year students, and graduate students (Masters and PhD). Needless to say, everyone is welcome!

This course begins with a brief introduction to classical calculus of variations and its appli- cations to classical problems such as geodesic trajectories and the brachistochrone problem. Then, we examine Hamilton-Jacobi equations, the role of convexity and the classical verifi- cation theorem. Next, we illustrate the lack of classical solutions and motivate the definition of viscosity solutions. The course ends with a brief description of the reinforcement learning problem and its connection with Hamilton-Jacobi equations.