Topology for Computing

1. Introduction; Part I. Mathematics: 2. Spaces and filtrations; 3. Group theory; 4. Homology; 5. Morse theory; 6. New results; Part II. Algorithms: 7. The persistence algorithms; 8. Topological simplification; 9. The Morse-Smale algorithm; 10. The linking number algorithm; Part III. Applications: 11. Software; 12. Experiments; 13. Applications.