This book is intended to present a new pedagogical approach to stochastic calculus and its applications in finance. Prof. Sondermann makes an easy to follow introduction to quadratic variation, Ito's formula etc. using only basic tools from real analysis. After he introduces the Ito calculus and Girsanov theorem, he presents some applications in finance, like the risk neutral valuation, the currency options and the HJM model.

The book has the advantage that it introduces the stochastic calculus without relying on very heavy background. However, by doing this, it loses most of the precision of statements, and makes the book more suitable for bed-time reading. The book has no index term(!!), which is quite surprising for a mathematical book these days. Exercise problems are presented only for the introductory chapter on real analysis, none though for the material dealing with stochastic calculus. I do not see the reason why Prof. Sondermann decided on having exercises on the preliminaries and none on the main material, stochastic calculus. The book has also its share of typos, so be careful.

On the nice features, I liked the careful discussion of the currency options paradox (Siegel-Paradox), and the change of numeraire.

I think that Prof. Sondermann succeeded in presenting stochastic calculus in an easy way, and now readers might feel more comfortable to start reading a more advanced book on stochastic calculus.