Combining sound mathematical principles with the necessary economic focus, Arbitrage Theory in Continuous Time is specifically designed for graduate students, and includes solved examples for every new technique presented, numerous exercises, and recommended reading lists for each chapter.
There are very few books in math which are worth reading from cover to cover and from which you can really learn a lot and which you truly enjoy reading. You could count them on your fingers and toes. To me, on the topic of financial mathematics, this book is in the same league as Spivak's Calculus and Rudin's Analysis. Buy it, read it, do the exercises (!) and enjoy the warm glowy feeling of actually knowing you have truly learned and understood something...