Part I. Geometric Constructions:
1. Examples and basic folds
2. Solving equations via folding
3. Origami algebra
4. Beyond classic origami
Part II. The Combinatorial Geometry of Flat Origami:
5. Flat vertex folds: local properties
6. Multiple-vertex flat folds: global properties
7. Counting flat folds
8. Other flat folding problems
Part III. Algebra, Topology, and Analysis in Origami:
9. Origami homomorphisms
10. Folding manifolds
11. An analytic approach to isometric foldings
Part IV. Non-Flat Folding:
12. Rigid origami
13. Rigid foldings
14. Rigid origami theory

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of the mathematics of folding.