Abstract: In the 1970’s, Thurston classified Mod(S) for higher genus surfaces in a widely circulated preprint, “remarkable for its brevity and richness.” This classification turns out to be a trichotomy (finite order, reducible, or pseudo-Anosov), just like the classification of automorphisms of the torus (finite order, reducible, or Anosov). The aim of this talk is to spell out his construction “for a large class of examples of diffeomorphisms in canonical form.” The real treasure of this construction is that it allows us to easily get our hands on pseudo-Anosov maps, a seemingly difficult task. As Thurston himself wrote “. . . it is pleasant to see something of this abstract origin made very concrete.” We motivate the construction by first classifying the automorphisms of the torus. Knowledge of basic linear algebra and hyperbolic geometry is assumed, and familiarity with mapping class groups will be helpful for following along.