We study the affine foliations on a compact surface in both cases : with a boundary and without a boundary. We connect between several ways of constructing these foliations. These ways are the first return map, the affine interval exchange (for a foliation which is not necessarily orientable), the train tracks with broken measures, the gluing affine foliations on surface with boundary, and the measured foliation on the universal covering with covering translation acting in affine ways. We study the injectivity of the applications with image in the space of equivalence classes of affine foliations which result from these various constructions.
