Discrete-time models. Arbitrage, martingale deflators, the fundamental theorem of asset pricing. Numéraires, equivalent martingale measures. Forwards, options, futures, bonds, interest rates. Attainable claims, market completeness. The Breeden-Litzenberger formula. Fourier pricing. Optimal stopping. Continuous-time models. Brief survey of Brownian stochastic calculus, Itô’s formula, martingale representation theorem, Girsanov’s theorem. Admissible strategies. Absolute and relative arbitrage. Existence of replicating strategies. Pricing and hedging via partial differential equations. Black-Scholes model. The implied volatility surface. Dupire’s formula. Stochastic volatility models.