Real affine structures on surfaces, moduli spaces and dynamics

A real affine structure on a surface is an atlas of charts on a topological surface, taking values in R^2 and whose transitions maps are real affine transformations. I will first try to give a variety of examples to gain familiarity with the concept and then discuss classical questions such as existence and geometry of their moduli space, mapping class group actions etc.

My ultimate goal will be to draw a conjectural picture of the geometry of the moduli space based on information coming from the dynamics of the geodesic foliations of affine surfaces.