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 "e;state of the art"e; 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.