From the reviews: "The book under review provides a thorough analysis of decomposable sets, the fixed point theory of maps on such sets, and applications of this theory. ... provides a comprehensive examination of the theory, starting with the background and preliminaries, going through the essence of the arguments of decomposability, and presenting a variety of applications. ... All in all the text is very useful to active researchers ... and to the general community including advanced students ... ." (Zvi Artstein, Mathematical Reviews, Issue 2005 k)

• Preliminaries.- Real and vector measures.- Preliminary notions.- Upper and lower semicontinuous multifunctions.- Measurable multifunctions.- Carathéodory type multifunctions.- Fixed points property for convex-valued mappings.- Decomposable sets.- Selections.- Fixed points property.- Aumann integrals.- Selections of Aumann integrals.- Fixed points for multivalued contractions.- Operator and differential inclusions.- Decomposable analysis.