Books on topological data analysis and persistent homology

Question

I am a physicist/data analyst and I am trying to get into topological data analysis. Needless to say, I severely lack background. My math education in this direction terminated at analytical geometry and the only time I encountered the concept of "space" was in Quantum Physics.

I need intro books, that will not assume a math degree to start building up understanding of topology and homology, graphs and mathematicians' version of group theory. Of course, if such books exist.

Thank you in advance for your suggestions!

Answer 1

Not exactly a book, but a reference I found helpful to start with "A Survey of Topological Machine Learning Methods"

https://www.frontiersin.org/articles/10.3389/frai.2021.681108/full

Bastian Rieck also has a number of online presentations.

Answer 2

For a list of all books I currently know about on applied topology, persistent homology, and topological data analysis, please see https://www.aatrn.net/affiliated-activities#h.cqfwvf3e8gq which has recently been duplicated from https://www.math.colostate.edu/~adams/advising/appliedTopologyBooks/. Any other additions are welcome!