There are already several excellent books on Malliavin calculus. However， most of them deal only with the theory of Malliavin calculus for Brownian motion， with as an honorable exception. Moreover， most of them discuss only the application to regularity results for solutions of SDEs， as this was the original motivation when Paul Malliavin introduced the infinite-dimensional calculus in 1978 in. In the recent years， Malliavin calculus has found many applications in stochastic control and within finance. At the same time， Levy processes have become important in financial modeling. In view of this， we have seen the need for a book that deals with Malliavin calculus for Levy processes in general， not just Brownian motion， and that presents some of the most important and recent applications to finance.