A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Jean-Daniel Boissonnat is a Research Director at the Institut national de recherche en informatique et en automatique, France. His research interests are in computational geometry and topology. He has published several books and more than 180 research papers, and is on the editorial board of the Journal of the ACM and of Discrete and Computational Geometry. He received the IBM award in Computer Science in 1987, the EADS award in Information Sciences in 2006 and was awarded an advanced grant from the European Research Council in 2014. He has taught at several universities in Paris and at the Collège de France.

Part I. Topological Preliminaries: 1. Topological spaces; 2. Simplicial complexes; Part II. Delaunay Complexes: 3. Convex polytopes; 4. Delaunay complexes; 5. Good triangulations; 6. Delaunay filtrations; Part III. Reconstruction of Smooth Submanifolds: 7. Triangulation of submanifolds; 8. Reconstruction of submanifolds; Part IV. Distance-Based Inference: 9. Stability of distance functions; 10. Distance to probability measures; 11. Homology inference.