One strategy in reading and taking apart the content of a physics or math text is to try and classify the parts of it into the above three points and sub-points. For each piece of text one is currently presented with, one can try and classify:

• data available to authors / processing of data / theory Read the text and classify aspects of it with this scheme
• in's and out's of a theory Is the text presenting a notion for modeling/is something modeled? When learning about a new theory (focusing on physical theories here), a point that it's extremely important is to watch out for what the observables of the theory are and what it really is that needs to be obtained. The point is that (unless we do it for the pure understanding/intuition of a natural phenomena) a theory is made to compute stuff. Many concepts which appear to be of importance on the surface are really just axillary notions that the theory sets up between input and output, and those can be substituted with other things. It's important to know what the theory is really about on the input and output level.
• Elaborations and mathematical theory The physical theory might set up the dynamics $F$, necessarily written down in mathematical terms, and much of the text is pandering on that mathematical object.
• Classifying definitions One can often identity certain types of definitions. Some have a flavor of enumeration (e.g. notion of a base are singled out to get hold of a spaces); or some are about generating more structure from previous definitions (spaces of automorphisms, induced product structures on the power set of groups, etc.); or some take a concept defined for the whole and refine it over the parts (=density). Ask: Is the text presenting a tool for computation? Crucial question regarding a definition one is reading: Why is a definition essential - is it for a computational strategy that can only be formulated with the help of this auxillary definition?

I'll try to think more about how to read. I think there could and maybe should be some sort of “literature critique theory of science/math books”
What I can recommend (at least for papers) is the strategy of reading an intro, the end, the intro again and then the whole thing.

• Read the content overview (get a feel for the structure of the book)
• Go through all the pages (get an impression for what it's about, how long the sections are etc.)
• Read the Introduction, read the end.
• - Judge if you have the basis to understand it
• - Judge if it's actually worth reading
• Read the whole thing (there'll be lots of things you don't get)
• (?) Take it apart according with an eye on the above ideas.
• (?) Take it apart according with an eye on the ideas in Perspective.
• How does it fit into a larger frame, to what extent is it captured on AoC.
• Do the exercises.

Perspective