I. Introduction -- 1. Foreign exchange markets -- II. Mathematical preliminaries -- 2. Elements of probability theory -- 3. Discrete-time stochastic engines -- 4. Continuous-time stochastic engines -- III. Discrete-time models -- 5. Single-period markets -- 6. Multi-period markets -- IV. Continuous-time models -- 7. Stochastic dynamics of forex -- 8. European options: the group-theoretical approach -- 9. European options, the classical approach -- 10. Deviations from the Black-Scholes paradigm I: nonconstant volatility -- 11. American Options -- 12. Path-dependent options I: barrier options -- 13. Path-dependent options II: lookback, Asian and other options -- 14. Deviations from the Black-Scholes paradigm II: market frictions -- 15. Future directions of research and conclusions.