This lecture covers the dynamics of singular Riemann surface foliations, focusing on compact Kähler manifolds. It discusses the existence of bidimensional currents and continuous forms, as well as the properties of Hahn-Banach spaces. The lecture also explores the construction of closed currents and the behavior of cluster points under foliation. Various propositions and theorems related to singular Riemann surface foliations are presented, along with extremal properties and the impact on leaves covered by discs.