If you want to learn the "stochastic calculus approach" to financial engineering, Nielsen is an excellent text. This isn't an intuitive watered-down treatment. It is formal and meticulous for readers who want to really master the material.

There are two chapter-length appendices covering measure theory, probability and Lebesgue integration (which probably should have been placed at the start of the book). I do not recommend reading the book without any background in these topics. Consider reading Bartle (1966) and parts of Resnick (1999) before proceeding to Nielsen. The first three chapters of Nielsen cover stochastic calculus. The next three develop derivatives pricing theory. The last chapter considers term structure models. This is a theoretical text, and not an easy read, but it will prepare you to understand the cutting-edge research in financial engineering today.