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In this talk, I will start with the fundamentals of Ito calculus. Then, we see that to handle more complicated problems, we need some mathematical tools beyond Ito calculus which is called Malliavin calculus. In the context of Malliavin calculus for Brownian motion, the derivative operator and the divergence operator, which is an extension of Ito integral, will be introduced. Then, the main results in Malliavin calculus will be discussed. I will conclude the talk with some recent applications of this theory in financial mathematics.