In this book, originally published in 1978, virtually everything known until 1978 about the hyperspaces 2X and C (X ) was gathered, organized, edited and presented in encyclopedic detail. With only a few exceptions, complete and readable proofs are given for all major results. Often these proofs are different than the original ones.

Topics include Whitney maps, which are the unifying organizational concept for the entire book, dimension, embedding in Euclidean space and in hyperspaces themselves, mappings between hyperspaces, selections on hyperspaces, the fixed point property, hyperspaces as other constructions (e.g., cones, suspensions, Cartesian products), arcwise disconnecting, arcwise accessibility, Whitney properties, the structure of the hyperspaces of hereditarily indecomposable continua, and spaces of sets such as compact convex sets, arcs, pseudo-arcs, etc. In addition, a number of new concepts and results about them originated in this book - for example, C*-smoothness, Whitney reversible properties, and C-determined continua.