Koszul cohomology computations were first used in algebraic geometry in 1984, and the interaction between the two has grown considerably since then. There being plenty introductory treatments available, Aprodu and Nagel (neither further identified) describe recent developments at a more advanced level. They discuss Voisin's proof of the generic Green conjecture and subsequent refinements, Syzgy schemes, the Hilbert scheme, the Koszul cohomology of a K3 surface, versions of the Syzygy conjecture, and other topics. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)