Sala Seminari (Dip. Matematica).
We provide an introduction to martingale optimal transport. In the context of the one-period version of the problem, we establish the Kantorovitch duality, we discuss the existence for the primal and the dual problems, and we provide the martingale version of the cyclic monotonicity condition together with of the one-dimensional Brenier theorem. We finally show the connection between continuous-time martingale transport and the Skorohod embedding problem, and we provide some applications.