... around which the book revolves.
Can I use this expression to say that the book is dealing with a subject, addressing an issue, or talking about something?
I'm open to suggestions if there is a better way to put it.
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Yes, you can use revolve this way; it would be used to mean:
5. to focus or center on.
It's a figurative usage. Revolve around [something] in its original physical sense means to move in a circular orbit around [something]. Applying the word outside the physical domain still brings to mind the physical connotation of orbiting, demonstrating that the topic is to the book as the sun is to a planet.