This book gives a comprehensive account of the arbitrage theory of financial derivatives in a mathematically precise way, but without the explicit use of abstract measure theory. It is aimed at graduate students and practitioners in economics, but will also be of interest to mathematicians and researchers in finance. The text is heavily orientated towards concrete computations and practical handling of stochastic differential equations, in their economic applications as well as in their purely mathematical context. The reader will find numerous worked-out examples as well as a large number of exercises.