A group of Gerry Schwarz’s colleagues and collaborators gathered at the Fields Institute in Toronto for a mathematical festschrift in honor of his 60th birthday. This volume is an outgrowth of that event, covering the wide range of mathematics to which Gerry Schwarz has either made fundamental contributions or stimulated others to pursue. The articles are a sampling of modern day algebraic geometry with associated group actions from its leading experts, with a particular focus on characteristic 0 and modular invariant theory. Contributors: M. Brion A. Broer D. Daigle J. Elmer P. Fleischmann G. Freudenberg D. Greb P. Heinzner A. Helminck B. Kostant H. Kraft R. J. Shank W. Traves N. R. Wallach D. Wehlau