Steven Carlip 2004-12-07 2005-01-24 Abstract In three spacetime dimensions, general relativity drastically simplifies, becoming a “topological” theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are still present. In this review, I summarize the rather large body of work that has gone towards quantizing (2+1)-dimensional vacuum gravity in the setting of a spatially closed universe. http://www.livingreviews.org/lrr-2005-1 Max Planck Institute for Gravitational Physics 2+1 gravity, Quantum gravity, Quantum cosmology Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe