The Hausdorff paradox
The Banach-Tarski paradox : duplicating spheres and balls
Hyperbolic paradoxes
Locally commutative actions : minimizing the number of pieces in a paradoxical decomposition
Higher dimensions
Free groups of large rank : getting a continuum of spheres from one
Paradoxes in low dimensions
Squaring the circle
The semigroup of equidecomposability types
Transition
Measures in groups
Applications of amenability
Growth conditions in groups and supramenability
The role of the axiom of choice.