Introductory reading

This article was originally written by Daniel Spitz for the STRUCTURES Wiki (captured October 2025).

This is a list of entries to the vastly growing literature in the field of topological data analysis, both from a theoretical and an applied point of view.

Literature on theory

A well-known theoretical introduction to the field. Carlsson: Topology and Data.

One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: Computing persistent homology.

A recently introduced topological summary better suited than persistence diagrams to statistically analyze persistent homology, the persistence landscape. Bubenik: Statistical topological data analysis using persistence landscapes.

Literature towards applications

A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: Computational topology: an introduction.

A general overview of persistent homology with an eye towards applications of different numerical libraries. In the supplementaries starting points for own numerical steps are given. Otter et al: A roadmap for the computation of persistent homology.

The mapper algorithm. Singh et al: Topological methods for the analysis of high dimensional data sets and 3d object recognition.