The Banach–Tarski Paradox

Published by Cambridge University Press, The Banach–Tarski Paradox 2nd Edition explores the mathematics of paradoxical geometric decompositions. Authors Grzegorz Tomkowicz and Stan Wagon examine both the nonexistence and existence of finitely additive measures across different settings.

The volume covers foundational examples such as the Hausdorff paradox, duplicating spheres and balls, and paradoxical constructions in hyperbolic space and higher dimensions. It also considers group actions, low-dimensional phenomena, and connections to amenable groups.

Written in terms suitable for undergraduate students, the text explains the paradox and its broader implications while highlighting unresolved mathematical questions that still await solution.