2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119438This article is based on the lectures given at the ``Ecole thematique de theorie ergodique'', at the C.I.R.M. in Marseille, in April 2006. We give a complete proof of a theorem of Kerckhoff, Masur and Smillie on the unique ergodicity of the directional flow on a translation surface in almost every direction. The proof follows the one presented in the survey of Masur and Tabachnikov.28 pages, 10 figures. SubmittedGeometric TopologyDynamical Systems32G15 (Primary) 30F30, 57R30, 37D40 (Secondary)text