Cieliebak (Ludwig Maximilians U., Germany) and Eliashberg (Stanford U., US) add refinements to the existence theorem for Stein structures and present new results concerning surrounding of subsets by J-convex hypersurfaces. The opening chapters explore the basic properties of J-convex functions and hypersurfaces, construct special hypersurfaces needed for extending J-convex functions over handles, and review several h-principles. Later chapters develop a Morse-Smale type theory for J-convex functions and introduce Weinstein manifolds and their deformations. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)