Well motivated; well explained; easy to understand! A great read; and still offering readers getting a deeper understanding! There are a number of reasons for this book: An understandable presentation of tools from probability and stochastic processes is especially timely.
With clear explanations, and with lots of examples and illustrations!
A useful first book, before turning to more specialized presentations!
While the subject has a long history and a multitude of applications, there is more recent buzz: It has been suggested that the recent turmoil in financial markets may be caused in part by poor understanding on the part of traders of the mathematical models for derivative trading.
The mathematical tools are widely used, but probably a lot less widely understood!

A bit of history: Stochastic processes is a theory started more than a hundred years ago (1900, Louis Bachlier, a Paris-PhD thesis under Poincare), then Albert Einstein's 1905 discovery of Brownian motion, Norbert Wiener's path-space integral (the 1920ties), K. Ito's integral & formula (the 1940ties) and Paul Samuelson-Merton-Black-Scholes 1974, a stochastic differential equation for option pricing: All mathematical tools devised for the purpose of predicting uncertain outcomes in the world around us: in financial engineering; in physics (quantum mechanics, diffusion & thermodynamics); in biology, and in other parts of our experience.
Review by Palle Jorgensen, March 2010.