Paul Lévy was an extraordinarily productive mathematician: in parallel with and independently from the Soviet mathematicians Kolmogorov and Khinchin, he discovered the major part of what is known today as the theory of stochastic processes. Among his contributions where the study of various properties of Brownian motion and the discovery of necessary and sufficient conditions in limit theorems for sums of independent random variables. He proved the Central Limit Theorem using characteristic functions, independently from Lindeberg who proved the same theorem using convolution techniques. He discovered the class of probability distributions known as "stable distributions" and proved the generalized version of the Central Limit Theorem for independent variables with infinite variance. He also introduced the notion of Brownian local time in the context of study of the properties of Brownian motion: today this concept plays a key role in the study of fine properties of diffusion processes. Michel Loeve gives a vivid description of Lévy's contributions: Paul Lévy was a painter in the probabilistic world. Like the very great painting geniuses, his palette was his own and his paintings transmuted forever our vision of reality... His three main, somewhat overlapping, periods were: the limit laws period, the great period of additive processes and of martingales painted in pathtime colours, and the Brownian pathfinder period."