The Banach-Tarski Paradox

Exploring the Banach-Tarski Paradox, this volume delves into its implications for measure theory and its interconnections with group theory, geometry, set theory, and logic. The updated edition features new proofs and results, including intriguing paradoxes in the hyperbolic plane related to Escher's artwork. A significant addition is a complete proof demonstrating that the circle can be squared using set theory, a long-standing challenge in mathematics. This comprehensive work unifies contemporary research while addressing numerous unsolved problems.