I an algebraic geometer, so the book I'm going to propose is about as far from my subject as it can be. Still I think that [Steele's book on stochastic calculus][1] is one of the best written mathematical books I know. It really makes you enjoy probability, starting from the simplest examples of random walks and building a lot of theory, like martingales, Brownian motion and Ito's integral. I almost wanted to change my subject when I was reading it! :-)


  [1]: https://www.amazon.de/Stochastic-Calculus-Financial-Applications-Mathematics/dp/0387950168/ref=sr_1_1?ie=UTF8&s=books-intl-de&qid=1279114527&sr=8-1