PhD course offered by the London Graduate School in Mathematical Finance Lecturer: Dr Markus Riedle (King's College London) Course summary: This course is an introduction top the theory of stochastic integration and the Itô calculus, a calculus applicable to functions of stochastic processes with irregular paths. The tools of stochastic calculus have found many applications in finance, engineering and physics. The course shall focus on the mathematical foundations of stochastic calculus, motivated in particular by applications to stochastic models in finance. We will focus on the theory for Brownian motions, but will indicate in the end how the theory can be extended to the larger class of semimartingales.