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I am interested in seeking out a reference for learning Persistence Homology (more of the theoretical mathematical aspects rather than the applications/ computer science aspects).

Currently, the two books I have attempted to read:

  • Elementary Applied Topology by R. Ghrist (Not very elementary at all)
  • Computational Topology - An Introduction by Herbert Edelsbrunner (also not an easy read)

One issue I faced reading the above two books is that the format of the books is like a story or "novel", rather than the theorem/proof style which is more organized. Also, the level of the books are quite difficult (despite the words "elementary" and "introduction").

Does anyone know a more gentle introduction to the subject of persistent homology? Ideally a self-contained book would be good.

Thanks a lot.

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