Translation surfaces of infinite-type, I

Compact translation surfaces are intimately linked to the geometry
of Teichmüller spaces and the billiard dynamics in rational polygons.
During this is two week mini-course (4 x 2h30) our aim is to introduce
translation surfaces of infinite type (that is non-compact) both through
geometric and dynamical points of view.

We will first present several examples that motivate the study of
translation surfaces of infinite type, in particular several models
of billiards. The next lectures will go through the topological,
geometrical and dynamical properties of these examples.