You use the same key/button to read the book to take it once it is open to read. This was done so that we could "borrow" a book to read it, but not have to steal it or take it if we don't want to.
Also, note that when the book is open to read, it will say "press
whatever" to take or "press
whatever" to steal, depending on ownership.
I say
whatever as my keys are remapped, I don't even remember what the stock Activate key is on the PC. I think it is E.