Groups and group actions are probably the most central objects in mathematics.Comprising volumes 31 and 32 of the ALM series (with further volumes forthcoming), the Handbook of Group Actions presents survey articles on the topic of group actions and how they appear in several mathematical contexts. The general subject matter is organized under the following sections: geometry, mapping class groups, knot groups, topology, representation theory, deformation theory, and discrete groups.The various articles deal with both classical material and modern developments. They are written by specialists in their respective subject areas, and addressed to graduate students who want to learn the theory, as well as to specialists as a reference.This is the first volume of the Handbook of Group Actions.