The 20th century saw the development of many of the key concepts and theories in algebraic geometry. However, the evolution of style and approach over time has rendered the original texts challenging for modern readers to decipher. Bridging the gap between classical and modern algebraic geometry, this book explains classical results using modern tools and language. The second edition has undergone significant expansion. This second volume includes new chapters on quartic surfaces, and on the theory of congruences of lines, the first known modern treatment of the work of E. Kummer and R. Sturm. Furthermore, the expanded bibliography now encompasses over 800 references, including references to results obtained in the 12 years since the publication of the first edition. This carefully crafted reference will continue to keep classical algebraic geometry results alive and accessible to new generations of graduate students and researchers today.

‘The first edition of this book has become the absolute reference for the treatment of classical algebraic geometry in modern terms. The new edition brings a series of important complements on most chapters, in particular on congruences of lines and quartic surfaces. In total this makes a very rich and complete book on the subject.’

Arnaud Beauville - Université Côte d'Azur