This book has the merit of trying to introduce modern math finance theory while avoiding too involved mathematics. However, by its lack of rigour, be it ambiguous notations or overlooked difficulties ( while some trivial things are explained too longly ), the book becomes useless when you start getting into more complex notions about half-way through it. Because the foundations it gives are weak, suddenly nothing makes sense anymore.
If you ever had a math lecture by a physicist then you know what I'm talking about when I say this is a bit of a cookbook. Overall a big disapointment, and there are some way better titles on the market like "Arbitrage Theory in Continuous Time".