Conway (mathematics, George Washington U.) presents a textbook for a year-long course with a semester of measure theory followed by a semester of functional analysis to prepare first-year graduate students for the PhD qualifying examination. Students are assumed to be familiar with the basic properties of metric spaces, in particular the concepts of compactness, connectedness, continuity, uniform continuity, and the surrounding results on these topics. Among his topics are elements of measure theory, a Hilbert space interlude, linear transformations, locally convex spaces, and Banach algebras and spectral theory. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)