The Banach-Tarski Paradox
This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up to date proofs and discusses many unsolved problems.
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This is one of the most enjoyable mathematics books I have seen. The collection of results is both unified and fascinating, and the bibliographic information very helpful.
The Hausdorff Paradox
The BanachTarski Paradox Duplicating Spheres and Balls
Locally Commutative Actions Minimizing the Number of Pieces in a Paradoxical Decomposition
Higher Dimensions and NonEuclidean Spaces
Free Groups of Large Rank Getting a Continuum of Spheres from One
Paradoxes in Low Dimensions
The Semigroup of Equidecomposability Types
Applications of Amenability Marczewski Measures and Exotic Measures
Growth Conditions in Groups and Supramenability
The Role of the Axiom of Choice
Euclidean Transformation Groups
Addendum to Second Printing