the origin of this book can be traced to courses on financial mathematics taught by us at the university of new south wales in sydney, technical university of warsaw (politechnika watszawska) and institut national polytechnique de grenoble. our initial aim was to write a short text around the material used in two one-semester graduate courses attended by students with diverse disciplinary backgrounds (mathematics, physics, computer science, engineering, economics and commerce). the anticipated diversity of potential readers explains the somewhat unusual way in which the book is written. it starts at a very elementary mathematical level and does not assume any prior knowledge of financial markets. later, it develops into a text which requires some familiarity with concepts of stochastic calculus (the basic relevant notions and results are collected in the appendix). over time, what was meant to be a short text acquired a life of its own and started to grow. the final version can be used as a textbook for three one-semester courses one at undergraduate level, the other two as graduate courses.
