  These lecture notes focus on the application of ideas of locality, in
particular Lieb-Robinson bounds, to quantum many-body systems. We consider
applications including correlation decay, topological order, a higher
dimensional Lieb-Schultz-Mattis theorem, and a nonrelativistic Goldstone
theorem. The emphasis is on trying to show the ideas behind the calculations.
As a result, the proofs are only sketched with an emphasis on the intuitive
ideas behind them, and in some cases we use techniques that give very slightly
weaker bounds for simplicity.
  This is a preliminary version of the lecture notes, with the goal of getting
the notes out close to the end of the school. Comments welcome.
