Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of t

This book is a comprehensive treatment of the theory of persistence modules over the real line. It presents a set of mathematical tools to analyse the structure

Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies

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

This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in t