This course provides an introduction to numerical methods for the valuation of financial derivatives and the theory behind. This includes in particular lattice methods, Monte Carlo simulation and variance reduction methods, simulation of stochastic differential equations, the finite difference and the finite element method. In contrast to the correspondent course on the Master level, the conceptual background is emphasized here on a high quantitative level. The course is open to participants in the Ph.D. program in Economics and Finance (PEF) as well as in the Ph.D. program in Management (PMA).