This book was planned and begun in 1929. Our original intention was that it should be one of the Cambridge Tracts, but it soon became plain that a tract would be much too short for our purpose.
Our objects in writing the book are explained sufficiently in the introductory chapter, but we add a note here about history and bibliography. Historical and bibliographical questions are particularly troublesome in a subject like this, which has applications in every part of mathematics but has never been developed systematically.