This book is a collection of research articles in algebraic geometry and complex analysis dedicated to Hans Grauert. The authors and editors have made their best efforts in order that these contributions should be adequate to honour the outstanding scientist. The volume contains important new results, solutions to longstanding conjectures, elegant new proofs and new perspectives for future research. The topics range from surface theory and commutative algebra, linear systems, moduli spaces, classification theory, Kähler geometry to holomorphic dynamical systems.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces. Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject. These proceedings reflect the topics of the lectures presented during the workshop 'Beauville surfaces and groups 2012', held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.

This volume contains a collection of research papers dedicated to Hans Grauert on the occasion of his seventieth birthday. Hans Grauert is a pioneer in modern complex analysis, continuing the il lustrious German tradition in function theory of several complex variables of Weierstrass, Behnke, Thullen, Stein, Siegel, and many others. When Grauert came on the scene in the early 1950's, function theory was going through a revolutionary period with the geometric theory of complex spaces still in its embryonic stage. A rich theory evolved with the joint efforts of many great mathematicians including Oka, Kodaira, Cartan, and Serre. The Car tan Seminar in Paris and the Kodaira Seminar provided important venues an for its development. Grauert, together with Andreotti and Remmert, took active part in the latter. In his career he has nurtured a great number of his own doctoral students as well as other young mathematicians in his field from allover the world. For a couple of decades his work blazed the trail and set the research agenda in several complex variables worldwide. Among his many fundamentally important contributions, which are too numerous to completely enumerate here, are: 1. The complete clarification of various notions of complex spaces. 2. The solution of the general Levi problem and his work on pseudo convexity for general manifolds. 3. The theory of exceptional analytic sets. 4. The Oka principle for holomorphic bundles. 5. The proof of the Mordell conjecture for function fields. 6. The direct image theorem for coherent sheaves."