Paul Wilmott on Quantitative Finance

John Hull is canon. Read it, live it, love it, keep it under your pillow. It is truly superb. Nassim Taleb's "Dynamic Hedging" is the finest book I'm aware of on the subject of actually trading/managing vol portfolios. It's REALLY good. And dense. "Paul Wilmott on Quantitative Finance" vol 1-3 are worth having as a reference, perhaps.

Any of Paul Wilmott's books. Either his single Introduction to Quantitative Finance, or his three volume set. His focus is on knowing where models work and where they break down, and how to avoid using them naively. http://wilmott.com/