1. a survey paper from 2004. This will be more or less the subject of the lectures, although I'll also do some more recent stuff.
2. Notes from a course I gave at UBC on probabilistic techniques in PDE. These notes are for continuous diffusions, but some of the ideas and techniques are at the basis of what is done for processes with jumps. The most useful sections are probably 14, 15, 22, 23, and 25-30.
3. I will spend a short (as short as possible) time on stochastic calculus for jump processes. Here are some notes on this.