Mathematicians and laymen alike have always been fascinated by simple numbers. This book is an introduction to a mythical book which might go under the name The Book of the Integers, that has on page n all of the interesting properties of the integer n. This introductory book stems from the collection of many years' casual accumulation of numerical facts, especially from the theory of numbers. No deep or profound mathematical background is required to understand the material, however much of it is sufficient out of the mainstream that even professional mathematicians may be unfamiliar with the results. There are many references to the literature to enable the reader to track down further information.