"The woman reads me the book."
Translation:Η γυναίκα μού διαβάζει το βιβλίο.
I believe "my woman" and "my wife" have the same meaning. Nevertheless, "a book" is "ένα βιβλίο", and "the book" is "το βιβλίο", with a definite article (if I'm not mistaken)
μού can only be "(to) me".
μου can come before a verb, meaning "(to) me", or after a noun, meaning "my".
Often, it's clear (e.g. αυτή μου διαβάζει ένα βιβλίο can only mean "she reads me a book" since the μου cannot belong to αυτή, which is not a noun), but when it's not, you can use the accented form to make clear that it's the "(to) me" meaning rather than the "my" meaning.
Indication of the used pronoun: