With the fast development of mathematical finance in recent years, stochastic calculus has been widely used in finance. This course is designed as the first courses in financial calculus for students having a good background in mathematics. After learning this course, students should understand the key concepts in stochastic analysis such as martingales and change of measure and some deep properties of Brownian motion process. The students should also be able to apply the basic methods and tools learning from this course such as the Ito’s formula and the Black-Scholes pricing formula in practical problems in finance.