I. Arithmetic and algebra. 1. The monkey and the coconuts ; 2. The calculus of finite differences ; 3. Palindromes : words and numbers
II. Plane geometry. 4. Curves of constant width ; 5. Rep-tiles ; 6. Piet Hein's superellipse ; 7. Penrose tiles ; 8. The wonders of a planiverse
III. Solid geometry and higher dimensions. 9. The helix ; 10. Packing spheres ; 11. Spheres and hyperspheres ; 12. The Church of the Fourth Dimension ; 13. Hypercubes ; 14. Non-Euclidean geometry
IV. Symmetry. 15. Rotations and reflections ; 16. The amazing creations of Scott Kim ; 17. The art of M. C. Escher
V. Topology. 18. Klein bottles and other surfaces ; 19. Knots ; 20. Doughnuts : linked and knotted
VI. Probability. 21. Probability and ambiguity ; 22. Nontransitive dice and other paradoxes ; 23. More nontransitive paradoxes
VII. Infinity. 24. Infinite regress ; 25. Aleph-null and aleph-one ; 26. Supertasks ; 27. Fractal music ; 28. Surreal numbers
VIII. Combinatorics. 29. Hexaflexagons ; 30. The Soma cube ; 31. The game of life ; 32. Paper folding ; 33. Ramsey theory ; 34. Bulgarian solitaire and other seemingly endless tasks
IX. Games and decision theory. 35. A matchbox game-learning machine ; 36. Sprouts and Brussels sprouts ; 37. Harary's generalized ticktacktoe ; 38. The new Eleusis
X. Physics. 39. Time travel ; 40. Does time ever stop? ; 41. Induction and probability ; 42. Simplicity
XI. Logic and philosophy. 43. The unexpected hanging ; 44. Newcomb's paradox ; 45. Nothing ; 46. Everything
XII. Miscellaneous. 47. Melody-making machines ; 48. Mathematical zoo ; 49. Gödel, Escher, Bach ; 50. Six sensational discoveries.
