In this talk, I will start with the fundamentals of Ito calculus. Then, we see that we need some mathematical tools beyond Ito calculus which is called Malliavin calculus to handle more complicated problems. Malliavin calculus, named after Paul Malliavin, extends the calculus of variations from functions to stochastic processes. This stochastic calculus of variations allows us to compute the derivatives of random variables which are useful in many cases. I will conclude the talk with some recent applications of this theory in financial mathematics.