Chapter 1. Money and markets
Chapter 2. Fair games
Chapter 3. Set theory
Chapter 4. Measurable functions
Chapter 5. Probability spaces
Chapter 6. Expected values
Chapter 7. Continuity and integrability
Chapter 8. Conditional expectation
Chapter 9. Lebesgue measure
Chapter 10. Martingales
Chapter 11. The Black-Scholes formula
Chapter 12. Stochastic integration
Solutions

The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the It calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results.