The aim of this book is to give a systematic introduction to the theory of surreal numbers based on foundations that are familiar to most mathematicians. I feel that the surreal numbers form an exciting system which deserves to be better known and that therefore an exposition like this one is needed at present. The subject is in such a pioneering state that it appears that there are many results just on the verge of being discovered and even concepts that still are waiting to be defined.

One might claim that one should wait till the theory of surreal numbers is more fully established before publishing a book on this subject. Such a comment reminds me of the classic joke about the person who is afraid of drowning and has vowed never to step into water until he has learned how to swim. In fact, the time is ripe for such a book and furthermore the book itself should contribute to developing the subject with the help of creative readers.

The subject has suffered so far from isolation with pockets of people in scattered parts of the world working on those facets of the subject that interest them. I hope that this book will play a role in eliminating this isolation and bringing together the mathematicians interested in surreal numbers.