"This course will give a brief introduction in stochastic calculus including Brownian motion, Ito integral, Ito process, Ito’s formula, stochastic differential equations; and its applications in finance which will mainly concentrate on Black-Scholes model including pricing contingent claims, deriving Black-Scholes-Merton PDE, Girsanov’s theorem and risk neutral pricing. After the course, students will have basic knowledge in stochastic analysis and ability to derive mathematical properties of stochastic models for financial systems formulated via stochastic differential equations, using the methods of stochastic calculus."