Volume Ⅰ Preface Gavril Farkas and Ian Morrison Logarithmic geometry and mo Dan Abramovich, ile Chen, Danny Cillam, Yuhao Huang, Martin Olsson, Matthew Satriano and Shenghao Sun Invariant Hilbert schemes Michel Brion Algebraic and tropical curves: comparing their mo spaces Lucia Caporaso A superfiaal working guide to deformations and mo F. Catanese Mo spaces of hyperbolic surfaces and their Weil-Petersson volumes Norman Do Equivariant geometry and the cohomology of the mo space of curves Dan Edidin Tautological and non-tautological cohomology of the mo space of curves C. Faber and R. Pandharipande Alternate compaaifications of mo spaces of curves Maksym Fedorchuk and David Ishii Smyth The cohomology of the mo space ofAbelian varieties Gerard van der Geer Mo of K3 surfaces and irreduable symplectic manifolds V Gritsenko, K. Hulek and C.K. Sankaran Normal functions and the geometry of mo spaces of curves Richard Hain Volume Ⅱ Parameter spaces of curves Joe Harris Global topology of the Hitchin system Tamas Hausel Differential forms on singular spaces, the minimal model program, and hyperboliaty of mo stacks Stefan Kebekus Contractible extremal rays on Mo,n Sean Keel and James McKernan Mo of varieties of general type Janos Kollar Singularities of stable varieties Sandor J Kovacs Soliton equations and the Riemann-Schottky problem I. Krichever and T. Shiota GIT and mo with a twist Radu Laza Good degenerations of mo spaces Jun Li Localization in Gromov-Witten theory and Orbifol Goov-Witten theory Chiu-Chu Melissa Liu From WZW models to modular functors Eduard Looijenga Shimura varieties and mo J.s. Milne The Torelli locus and spe subvarieties Ben Moonen and Frans Oort Volume Ⅲ Birational geometry for nilpotent orbits Yoshinori Namikawa Cell decoitions of mo space, lattice points and Hurwitz problems Paul Norbury Mo of abelian varieties in mixed and in positive characteristic Frans Oort Local models of Shimura varieties, I. Geometry and combinatorics Georgios Pappas, Michael Rapoport and Brian Smithling Generalized theta linear series on mo spaces of vector bundles on curves Mihnea Popa Computer aided unirationality proofs of mo spaces Frank-Olaf Schreyer Deformation theory from the point of view of fibered categories Mattia Talpo and Angelo Vistoli Mumfords conjecture -- a topological outlook Ulrike Tillmann Rational parametrizations of mo spaces of curves Alessandro Verra Hodge loci Claire Voisin Homological stability for mapping class groups of surfaces Nathalie Wahl