Topological Data Science

Topological Data Science develops a rigorous, accessible path from geometric and topological intuition to formal definitions, algorithms, statistical inference, and practical learning from complex data. It explains how data acquire shape through notions of proximity, incidence, compatibility, and transformation, and shows how persistent homology and related methods reveal structure that ordinary summaries can miss. Designed for advanced students, researchers, and practitioners, the book combines careful derivations, worked examples, visual arguments, computational procedures, exercises, and full resolutions. It emphasizes honest interpretation, reproducible analysis, and the connection between representation, computation, inference, and scientific claims.