When I ask someone whether they have read a certain book, they often reply with something along the lines of: "Yes. Well, actually I listened to the audio book". Or vice versa.
What is the verb that I could use that would
The word would fit in to the following blank:
Have you ____ Mastery by Robert Greene?
There are a few you could use, although they are not as common as the specific one for the medium in question—and they're more often used when you already know that somebody has started something.
Have you finished Mastery by Robert Greene?
Have you consumed Mastery by Robert Greene?
The latter is using the Merriam-Webster's sense of consumed that means "to enjoy avidly," as in "mysteries, which she consumes for fun."
And, given that, you could also simply ask if they've enjoyed the book—although that seems a bit odd if you're not after a "review."
It might be strange to use either of those verbs without context, however. If you're asking somebody in general, even if you know they actually read some and listen to others, it's common to simply say read.
Of course, if they are text books or school books, you can also use the verb studied.
