I decided to write a review after reading the other reviews and getting a sense that they are being rather unfair. The poor rating reviews appear to be based on the reviewers' dislike for the book's style and not so much on content.
Studying quantitative finance at a postgraduate level, there is a lot that is assumed. Thus I have been looking for quite some time for a good book that ties probability theory to calculus in a step by step way that enables me to understand it from first principles. This is the first book I have seen after a long search that really makes no assumptions and covers the topics really well.
Combining this book with the Schaum series book "Probability, Random Variables, and Random Processes" has really helped me understand the material very well.