In the past, representatives of the L,vy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays, the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general L,vy processes. Researchers and practitioners in physics, meteorology, statistics, insurance and finance have rediscovered the simplicity of L,vy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world.