Abstract: Malliavin calculus has been one of the most attractive topics in the domain of stochastic analysis in recent years.It is intrinsically a kind of“relative”differential calculus for functionals of paths of Brownian motion.In the sense of this differentiation, many interesting functionals such as solutions of It s equations become“smooth”and the existence of smooth densities of their distributions can be established.This technique has opened a vast field for using probabilistic method to solve various analytical problems.It has been successfully applied to the regularity of the heat kernels for hypoelliptic differential operators,the filtering theory and statistical physics as well as many other fields. So far as we know,there have been three formulations of Malliavin caloulus:the martingale calculus and symmetric diffusion semi-group method introduced by Malliavin and improved by Stroock,the Sobolev space formulation given by Shigekawa and the Girsanov transformation approach initialed by Bismut.In this expository paper,we mainly follow the formulation of Shigekawa.At the same time,we point out the equivalence of those three formulations and the advantages as well as possibilities of applications for each formulation.