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 and to establish the stability of such
modules, providing a sound mathematical framework for the study of
persistence diagrams. Completely self-contained, this brief
introduces the notion of persistence measure and makes extensive
use of a new calculus of quiver representations to facilitate
explicit computations. Appealing to both beginners and experts in
the subject, The Structure and Stability of Persistence Modules
provides a purely algebraic presentation of persistence, and thus
complements the existing literature, which focuses mainly on
topological and algorithmic aspects.
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