Okay, there are numerous financial engineering textbooks on the market. A lot of them are excellent, and this one is too. How do you pick the right one for self study or for a course you may need to teach? My job is to help you answer that question, so what can I say about this book?

It is a practical introduction to the mathematics of financial engineering. It has no introductory narrative about financial markets, the roles of market participants or basic derivative instruments—the material covered in Kolb (2007) or the first half of Hull (2005). It focuses on the pricing material covered in the second half of Hull, and it does a much better job of it. If you want a serious introduction to the mathematics of derivatives pricing, consider this an excellent Hull alternative.

Accordingly, the book should be used in the second semester of a two semester course on derivatives or it should be used by someone who already has considerable familiarity with derivatives markets. The level is suitable for a senior college student studying mathematics or a first year graduate student studying finance.

Back's focus is on showing readers how to use the fundamental theorem of asset pricing to value instruments, which is pretty much what you want to know to be a financial engineer. He doesn't bother with measure theory or the nitty-gritty probability theory that often bogs down other books. There is no talk of sample spaces, filtrations or Radon-Nikodym derivatives, which aren't really relevant for practical financial engineering anyway. Results tend to be stated rather than proven, but the author is careful to develop concepts in a logical and largely intuitive manner. He also provides VBA code and plenty of exercises to practice concepts on.

The author's real strength is motivating individual concepts. He is not as strong at the "forest-for-the-trees" sort of overall motivation. If you already have a general familiarity with financial engineering (or the book will be used in a course where the professor can provide such macro motivation) you won't mind at all.