It is quite advanced: "The essential prerequisites for reading this book are a rigorous course in probability theory (on Masters or Ph.D. level), an excellent command of undergraduate linear algebra, and general familiarity with basic notions about metric, normed and Hilbert spaces and linear operators. Knowledge of measure theory is not essential but would be helpful."
The High Dimensional Probability textbook is one of my all time favorites. The elegant mix of probability, geometry, and linear algebra can generate some really non-intuitive insights. The intuitions developed are also pretty useful for reasoning about modeling in a lot of applications
Skimming through, this looks like an attempt at a foundation with a bunch of applications. Meanwhile, it looks to me that the applications can generally be explained without the fairly advanced foundation (e.g. stochastic block model, concentration inequalities, and so on).<p>So, the "with applications to Data Science" is right, and should not be confused with "a bunch of advanced maths that you need to know in order to understand these applications".