Thurston's classification of surface diffeomorphisms

After one semester’s work we finally reached the first crown jewel, Thurston's classification of surface diffeomorphisms. Based on their action on the compactified Teichmuller space, the surface mapping classes are classified into three types: periodic, reducible and pseudo-Anosov. We will especially talk about what happens to the measured foliation in the pseudo-Anosov case, based on a decomposition of surfaces into foliated rectangles.