Leoni (mathematical sciences, U. of Minnesota) provides a textbook that explores Sobolev spaces from a novel viewpoint: by examining them as the natural development of monotone, absolutely, continuous, and BV functions of one variable. The approach, the author notes, is intended to render the majority of the text readable with a prerequisite course in functional analysis. The book is divided into two sections. The first is devoted to studying the functions of one variable. The second section is more classical in approach and in addition to Sobolev functions also includes chapters on BV functions, symmetric rearrangement, and Besov spaces. More than 200 exercises are included. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)