Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
Not horribly written, on one of the most annoying topics in 20th-century mathematics. If you're interested in hyperbolic geometry, this book is cool to look at. I have no idea why anyone cares about amenable groups.