Varolin (mathematics, State U. of New York-Stony Brook) presents certain parts of the basic theory of Riemann surfaces through methods of complex analytic geometry, many of them developed over the past 50 years or so. The textbook is for graduate students who are interested in analysis and geometry and have completed basic first courses in real and complex analysis, differentiable manifolds, and topology. Among the topics are functions on Riemann surfaces, complex differential forms, uniformization, and the Riemann-Roch theorem. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)