Financial Mathematics is an exciting, emerging field of application. The five sets of course notes in this book provide a bird's eye view of the current state of the art and directions of research. For graduate students it will therefore serve as an introduction to the field while reseachers will find it a compact source of reference. The reader is expected to have a good knowledge of the basic mathematical tools corresponding to an introductory graduate level and sufficient familiarity with probabilistic methods, in particular stochastic analysis.