The purpose of the book is to present the Malliavin-Skorohod calculus for additive processes, that is, processes with independent increments; in other words, Levy processes without the hypothesis of stationarity of increments. This will be the addition of Malliavin calculus for Gaussian processes and Malliavin calculus for Poisson random measures. The second is the application of the previous theory to finance, concretely, to stochastic volatility jump diffusion models, in order to solve problems related with pricing and hedging via Clark-Ocone formula, computation of sensitivities, obtaining useful price decompositions (Hull and White type formulas) and local risk minimizing strategies.