Mathematicians McDuff (emerita, Columbia U.) and Salamon (ETH, Zurich, Switzerland) set out the fundamental theorems in the theory of J-holomorphic curves in full and rigorous detail, and introduce current work in symplectic topology, where the theory has become of great importance. Here they revise the 2004 first edition to correct errors and to update the current work in symplectic topology being introduced. They provide more material than can be taught in a one-semester graduate course, so instructors can (and must) design any of several different courses by choosing what to use. The topics include moduli spaces and transversality, compactness, stable maps, Gromov-Witten invariants, and quantum cohomology. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)