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

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a conc

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

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