Large numbers have always been a source of wonder and many questions are raised about them. 'What comes after billions?' or 'How do the relative sizes of an atom and a man compare to the relative sizes of a man and the sun?' The author has answered some of these questions by explaining the arithmetic and the uses of large numbers in a way which introduces the reader to the horizons of modern mathematics. Using large num bers as a unifying theme and employing only the simplest materials, the author provides the reader with an understanding for numbers, their magnitude, and their growth. The reader is introduced to exponents, computation, number theory, and to the rapidity of growth of sequences. Several historical passages reveal mathematics as a living thing that grows and changes with the generations. Tables listing interesting and useful numbers in the physical universe are appended.