1 - Brownian motion
1.1 Definition and properties
1.2 Derived Processes
1.3 Simulation
2 - Martingales in continuous time
2.1 Definition and properties
2.2 Optional sampling theorem
3 - Stochastic Integration
3.1 Definition and properties
3.2 Lema of Itô
3.3 Girsanov's theorem
3.4 Martingale Representation Theorem
4 - Introduction to differential stochastic equations
4.1 Itô's Stochastic Differential Equations
4.2 Linear Differential Equations
4.3 Digital solutions
5 - Applications of stochastic calculus to Finance
5.1 The Black-Scholes formula
5.2 Risk neutral measures
5.3 Pricing Exotic options
5.4 Pricing American options