The present volume contains, together with numerous addition and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the -Centro Internazionale Mate matico Estivo-. The treatment has the character of a monograph, and presents various novel features, both in form and in substance; these are indicated in the notes which will be found at the beginning and end of each chapter, Of the nine parts into which the work is divided, the first four are essentially differential in character, the next three deal with algebraic geometry, while the...