This book was written to furnish a starting point for the study of algebraic geometry. The topics presented and methods of presenting them were chosen with the following ideas in mind; to keep the treat- ment as elementary as possible, to introduce some of the recently devel- oped algebraic methods of handling problems of algebraic geometry, to show how these methods are related to the older analytic and geometric methods, and to apply the general methods to specific geometric prob- lems. These criteria led to a selection of topics from the theory of curves, centering around birational...