Surveys the very active field of Calabi-Yau varieties from a geometric and arithmetic perspective

Includes four introductory lectures that can be used by graduate students and other researchers as a guide to the field

Contains a varied selection of topics from pure arithmetic questions to geometric questions to Hodge theory

Includes supplementary material: [...]

.-Preface.-Introduction.-List of Participants.- K3 and Enriques Surfaces (S. Kondo).- Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi¿Yau Varieties (J.D. Lewis).- Two Lectures on the Arithmetic of K3 Surfaces (M. Schütt).- Modularity of Calabi¿Yau Varieties (N. Yui).- Explicit Algebraic Coverings of a Pointed Torus (A. Anema, J. Top).- Elliptic Fibrations on the Modular Surface Associated to ¿1(8).- Universal Kummer Families over Shimura Curves (A. Besser, R. Livné).- Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Characteristic (I.V. Dolgachev).- Picard-Fuchs Equations of Special One-Parameter Families of Invertible Polynomials (S. Gährs).- A Structure Theorem for Fibrations on Delsarte Surfaces (B. Heijne, R. Kloosterman).- Fourier¿Mukai Partners and Polarised K3 Surfaces (K. Hulek, D. Ploog).- On a Family of K3 Surfaces with S4 Symmetry (D. Karp, J. Lewish, D. Moore, D. Skjorshammer, U. Whitcher).- K1ind of Elliptically Fibered K3 Surfaces (M. Kerr).- A Note About Special Cycles on Moduli Spaces of K3 Surfaces (S. Kudla).- Enriques Surfaces of Hutchinson¿Göpel Type and Mathieu Automorphisms (S. Mukai, H. Ohashi).- Quartic K3 Surfaces and Cremona Transformations (K. Oguiso).- Invariants of Regular Models of the Product of Two Elliptical Curves at a Place of Multiplicative Reduction (C. Schoen).- Dynamics of Special Points on Intermediate Jacobians (X. Chen, J.D. Lewis).- Calabi¿Yau Conifold Expansions (S. Cynk, D. van Straten).- Quadratic Twists of Rigid Calabi¿Yau Threefolds over Q (F.Q. Gouvêa, I. Kimming, N. Yui).- Counting Sheaves on Calabi¿Yau and Abelian Threefolds (M.G. Gulbrandsen).- The Serge Cubic and Borcherds Products (S. Kondo).- Quadi-Modular Forms Attached to Hodge Structures (H. Movasati).- The Zero Locus of the Infinitesimal Invariable (G. Pearlstein, Ch. Schnell).