The proceedings from the Abel Symposium on Geometry of Moduli held at Svinøya Rorbuer Svolvær
in Lofoten in August 2017 present both survey and research articles on the recent surge of
developments in understanding moduli problems in algebraic geometry. Written by many of the
main contributors to this evolving subject the book provides a comprehensive collection of new
methods and the various directions in which moduli theory is advancing. These include the
geometry of moduli spaces non-reductive geometric invariant theory birational geometry
enumerative geometry hyper-kähler geometry syzygies of curves and Brill-Noether theory and
stability conditions. Moduli theory is ubiquitous in algebraic geometry and this is reflected
in the list of moduli spaces addressed in this volume: sheaves on varieties symmetric tensors
abelian differentials (log) Calabi-Yau varieties points on schemes rational varieties
curves abelian varieties and hyper-Kähler manifolds.
