This research school in Geometry and Dynamics on surfaces, revolves around two classic and very current themes which are : – the topological and ergodic dynamics of geodesic and horocylic flows ; – random walks on groups. Indeed, starting from the work of Eskin-Mirzakhani on orbit closures of the upper triangular subgroup of SL(2,R) on strata of Abelian differentials ten years ago, recent years have witnessed some interplay between the dynamical theory of surfaces and the one of random walks on groups. One of the objectives of the research school is to give young researchers the opportunity to learn about both topics, in view for them to be able to deal with emerging questions.