This book provides an overview of the latest developments
concerning the moduli of K3 surfaces. It is aimed at algebraic
geometers, but is also of interest to number theorists and
theoretical physicists, and continues the tradition of related
volumes like "The Moduli Space of Curves" and "Moduli of Abelian
Varieties," which originated from conferences on the islands Texel
and Schiermonnikoog and which have become classics. K3 surfaces and
their moduli form a central topic in algebraic geometry and
arithmetic geometry, and have recently attracted a lot of attention
from both mathematicians and theoretical physicists. Advances in
this field often result from mixing sophisticated techniques from
algebraic geometry, lattice theory, number theory, and dynamical
systems. The topic has received significant impetus due to recent
breakthroughs on the Tate conjecture, the study of stability
conditions and derived categories, and links with mirror symmetry
and string theory. At the same time, the theory of irreducible
holomorphic symplectic varieties, the higher dimensional analogues
of K3 surfaces, has become a mainstream topic in algebraic
geometry. Contributors: S. Boissiere, A. Cattaneo, I. Dolgachev, V.
Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S.
Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G.
Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I.
Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.
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