The objective of the course is to introduce basic stochastic models and techniques used in mathematical finance. The first half of the course is dedicated to discrete-time models, the other half to their continuous-time counterparts. The topics covered include pricing and hedging in binomial models and Black-Sholes models, fundamental theorems of asset pricing, martingales, Brownian motion, stochastic integration, Itô rule. Depending on the progress in class, we also briefly discuss SDE?s as they appear in continuous-time models.