In late 1917 Pierre Fatou and Gaston Julia each announced several results regarding the iteration ofrational functions of a single complex variable in the Comptes rendus of the French Academy of Sciences. These brief notes were the tip of an iceberg. In 1918 Julia published a long and fascinating treatise on the subject, which was followed in 1919 by an equally remarkable study, the first instalIment of a three part memoir by Fatou. Together these works form the bedrock of the contemporary study of complex dynamics. This book had its genesis in a question put to me by Paul Blanchard. Why did...