This book is based on notes that Schwartz made when he taught an undergraduate seminar on surfaces at Brown University in 2005. Students should have completed a semester each in real analysis, abstract algebra, and complex analysis, though he embeds a kind of mini-course on complex analysis in this text. He discusses surfaces from many perspectives, such as metric spaces, triangulated surfaces, and hyperbolic surfaces as well as some matter only tangential to surfaces. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)