。
She went to Italy to research music.
Literal
She [topic-は] music [object-を] research [for-ために] Italy [to-へ] went.
音楽を研究する uses the verbal frame for 'research music' — Japanese can also nominalize this as 音楽研究 ('music research') and the meaning hardly shifts. The clause version reads slightly more dynamic, the noun version slightly more formal-academic. ~ために takes a verb's dictionary form when the purpose is itself a verbal action, and Italy's draw for music researchers comes especially from its operatic and Renaissance heritage — Milan's La Scala, the Florence conservatory, the bel canto vocal tradition.