Learning a new topic also entails learning its terminology. As a newbie to the subject, I'm amused by chapter headings like "Abstract Simplicial Complex" that seem like an oxymoron :-)
A simplicial complex is a bunch of simplices stuck together (adjacent simplices might share a lower-dimensional simplex as a common boundary).
https://en.wikipedia.org/wiki/Simplicial_complex
I’m not convinced “abstract” is a good word here, but what they mean is that it doesn’t have any metrical/geometric relationships beyond the graph structure.