The course will cover most of the standard materials in continuous-time finance such as the Black-Scholes-Merton framework of derivatives pricing, Merton's dynamic programming approach and the Cox-Huang martingale approach of solving dynamic optimal portfolio choice problems, the term structure models of Vasicek, Cox, Ingersoll, and Ross (CIR), and Heath, Jarrow, and Morton (HJM), numerical methods for pricing derivatives and solving partial differential equations.