Notes based on a series of lectures delivered at the Nankai Institute of Mathematics (Tianjin, China) in fall 1998 on various aspects of Hilbert's Third Problem, in particular its relation to homological algebra and algebraic K -theory. Based largely on the work of Dupont (Aarhus U., Denmark) and the late Chih-Han Sah, the work starts from Dehn's classical solution of the problem: Are two Euclidean polyhedra with the same volume "scissors-congruent," that is, can they be subdivided into a finite number of pairwise congruent pieces? Includes previously unpublished material. Annotation c. Book News, Inc., Portland, OR (booknews.com)