The author presents a selection of pieces from his Scientific American "Mathematical Games" column, presenting puzzles and concepts that range from arithmetic and geometrical games to the meaning of M.C. Escher's artwork.

Preface -- 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.