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These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume "scissors-congruent", i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of gr

Tetrahedra. --- Volume (Cubic content) --- Characteristic classes. --- Classes, Characteristic --- Differential topology --- Cubic measurement --- Volumetry --- Units of measurement --- Geometry, Solid --- Polyhedra --- Tetrahedra --- Characteristic classes

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