In recent years, research in K3 surfaces and CalabiYau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physicsin particular, in string theory. The workshop on  Arithmetic and Geometry of  K3 surfaces and CalabiYau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of CalabiYau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated.

Unlike most other conferences, the 2011 CalabiYau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.

.-Preface.-Introduction.-List of Participants.- K3 and Enriques Surfaces (S. Kondo).- Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on CalabiYau Varieties (J.D. Lewis).- Two Lectures on the Arithmetic of K3 Surfaces (M. Schütt).- Modularity of CalabiYau 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).- FourierMukai 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 HutchinsonGöpel 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).- CalabiYau Conifold Expansions (S. Cynk, D. van Straten).- Quadratic Twists of Rigid CalabiYau Threefolds over Q (F.Q. Gouvêa, I. Kimming, N. Yui).- Counting Sheaves on CalabiYau 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).