This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis.

Rene Schilling s notes are an expanded version of his course on Levy and Levy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Levy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Levy-Ito decomposition. On the other, it identifies the infinitesimal generator of the Levy...