In the summer of 1976 Kenneth Appel and Wolfgang Haken of the University of Illinois announced that they had solved the Four-Color Problem. Suddenly what had been known to several generations of mathematicians as the Four-Color Conjecture had become the Four-Color Theorem.Since it had been a conjecture for over one hundred years that all maps are four-colorable, and since a great deal of mathematics was done in attempts to solve the Four-Color Conjecture, it will be called a conjecture rather than a theorem throughout most of this book.