"Anche tu hai il libro."
How do you know when 'anche' means 'also' and when it means 'even'. The context doesn't always make it clear. 'Anche io' means 'me too', but in this sentence it doesn't mean 'You too have the book', it means 'Even you have the book'. Is it just one of those words that isn't always clear, like in English when you ask, "Do you mean funny strange or funny ha ha?"
It depends on the context, unfortunately. Anyway, the direct translation of "even" is "persino", "perfino", I would translate here "Anche" as "as well" or "too", but "even" could work.