The main goal will be to present a proof that mapping class groups have finite asymptotic dimension. This will give me a good excuse to talk about projection complexes, asymptotic dimension, curve complexes and subsurface projections. Most of this will be self-contained, with few "black boxes". Reading list: Hyperbolic groups and spaces, from the standard books like Bridson-Haefliger or Kapovich-Drutu Some familiarity with mapping class groups, e.g. the first 3 sections of Farb-Margalit