Some fundamental properties related to Lévy processes are discussed. Topics include infinitely divisible distributions, Lévy-Khintchine formula, Poisson random measures, Lévy-Itô decomposition, series representations, and density transformations. 1 Basic properties • In short, a Lévy process X = {Xt}t≥1 is a R-valued process with independent and stationary increments whose paths are right-conti...