Leonhard Euler and his three "great" friends
What is a polyhedron?
The five perfect bodies
The Pythagorean brotherhood and Plato's atomic theory
Euclid and his elements
Kepler's polyhedral universe
Euler's gem
Platonic solids, gold balls, Fullerenes, and geodesic domes
Scooped by Descartes?
Legendre gets it right
A stroll through Königsberg
Cauchy's flattened polyhedra
Planar graphs, geoboards, and brussels sprouts
It's a colorful world
New problems and new proofs
Rubber sheets, hollow doughnuts, and crazy bottles
Are they the same, or are they different?
A knotty problem
Combing the hair on a coconut
When topology controls geometry
The topology of curvy surfaces
Navigating in n dimensions
Henri Poincaré and th ascendance of topology
The million-dollar question.