In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged."

Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index.

The theory of surfaces has reached a certain stage of completeness and major efforts concentrate on solving concrete questions rather than developing further the formal theory. Many of these questions are touched upon in this classic volume: such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface. First printed in 1905 after the untimely death of the author, this work has stood for most of this century as one of the classic reference works in geometry.

In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.

Die zunehmenden Fahigkeiten von Rechnersystemen ermoglichen den Einsatz komplexer mathematischer Methoden fur Anwendungen aus dem Bereich der Graphischen Datenverarbeitung und des Computer Aided Design (CAD). Der effektive Einsatz dieser Methoden in den verschiedenen Darstellungsbereichen der Graphischen Datenverarbeitung, wie CAD-, Animations- oder Visualisierungssystemen, erfordert eine intensive Abstimmung und Zusammenarbeit der Fachgebiete Mathematik und Informatik sowohl in der Forschung als auch in der industriellen Anwendung. Mit der Zielsetzung, einerseits die mathematisch-geometrischen Grundlagen und andererseits die Anwendungen geometrischer Verfahren im Graphik- und CAD-Bereich darzustellen und zu diskutieren, veranstaltete das Darmstadter Zentrum fur Graphische Datenverarbeitung (ZGDV) in Zusammenarbeit mit der Fraunhofer-Arbeitsgruppe fur Graphische Datenverarbeitung (FhG-AGD) und der Technischen Hochschule Darmstadt vom 28. bis 30. Marz 1990 den Workshop, aus dem die Beitrage dieses Buches hervorgehen."