Abstarct: Levy Process is one of the most important and most widely used process in financial mathematics.This process begins when the stock market pulled down market ,a sudden jump in prices will occur . Such markets for stochastic modeling process used levy so the issues surrounding this procedure to model the stock markets is important. In this essay, at first the process itself had been introduced and Then its relation with poisson,Compound poisson process, Infinitely Divisibility was stated. In the last chapter for A Martingale Representation for the Maximum of a levy process presented.