Beyond the classical theory, this course will cover some recent extensions of the theory of Markov Decision Processes (MDP) to the optimization of various risk measures. Starting from Bellman's Dynamic Programming, we will introduce the Distributional approach. We will then discuss how risk measures are usually defined, and discuss their properties. We will then show how classical algorithms based on backward induction can, or cannot, be adapted. The theory will be illustrated on classical or less classical benchmarks such as for example labyrinths or the inventory management problem. We will finally consider the foundations of reinforcement learning, starting with the vanilla bandit problem and then considering general approaches for MDPs. The course will be balanced between theory and practice, with exercice sessions dedicated to the implementation of the course’s algorithmic content.