There are some difficulties to overcome in order to convince persons that the subject of this book is worth knowing something about. George Boole's theory of probability has had an extremely bad press for more than 100 years. It has almost universally been considered to be too complicated to understand, too difficult to calculate, and wrong in addition. As evidence that this is true, try and find a book on probability in, say, the 20th century which has any material on Boole's theory of probability. This is quite remarkable treatment for a person as distinguished as George Boole. In fact, his theory is not wrong, it is quite easy to make the calculations after a few simple emendations, it can solve a number of important problems which cannot be handled by the orthodox theory of probability, and there are quite a few areas in which these problems arise. In the following panes we will try and convince skeptics that there are good reasons for believing that a book on the subject is justified.