。
She went to Italy to study music.
Literal
She [topic-は] music [object-を] study [for-ために] Italy [to-へ] went.
The plain ~ために form: the standard hiragana writing of the purpose construction. Verb dictionary form + ために conveys 'in order to do X.' This is the most neutral of Japanese's many purpose expressions — not as formal as ~目的で, not as casual as the verb-stem に before motion verbs. The destination here, Italy, suggests classical voice or perhaps Renaissance-era composition.