This example from Mastronarde is meant to illustrate the usage of the pronoun αὐτόσ
τὰ βιβλία ἦν αὐτοῦ τοῦ διδασκάλου, οὺ τοῦ ποιητοῦ.
The books belonged to the teacher himself, not to the poet.
What I don’t understand is the third word: ἦν.
I don’t even know what part of speech it is. And especially I don’t know if it performs a grammatical function in relation to the pronoun αὐτόσ.