This course provides the necessary background from measure-theoretic probability theory, which is essential for developing the methods of continuous-time finance, based on stochastic analysis. Main topics: measure spaces and probability structures, integration, information structures (sample spaces, event trees, sigma- algebras, and partitions), random variables, conditioning and independence, probability distributions and change of measure, convergence of random variables, random sampling, the binomial model and the connection between equilibrium asset pricing and martingales in discrete time.