This book on complex algebraic curves is intended to be accessible to any third year mathematics undergraduate who has attended courses on algebra, topology and complex analysis. It is an expanded version of notes written to accompany a lecture course given to third year undergraduates at Oxford. It has usually been the case that a number of graduate students have also attended the course, and the lecture notes have been extended somewhat for the sake of others in their position. However this new material is not intended to daunt undergraduates, who can safely ignore it. The original lecture course consisted of Chapters 1 to 5 (except for some of §3.1 including the definition of intersection multiplicities) and part of Chapter 6, although some of the contents of these chapters (particularly the introductory material in Chapter 1) was covered rather briefly.

Each section of each chapter has been arranged as far as possible so that the important ideas and results appear near the start and the more difficult and technical proofs are left to the end. Thus there is no need to finish each section before beginning the next; when the going gets tough the reader can afford to skip to the start of the next section.

The main aim of the course was to show undergraduates in their final year how the basic ideas of pure mathematics they had studied in previous years could be brought together in one of the showpieces of mathematics.