She invited me to the ballet.

Literal

She [topic-は] me [object-を] ballet [to-に] invited [for my benefit-てくれた].

バレエ is a French loanword (from ballet), pronounced /baree/ — distinct from the also-extant バレー /baree-/ (volleyball, from English) by a single mora and stress pattern, a classic katakana minimal pair that trips up beginners. に marks the event as the destination of the invitation (a productive use of に for events, parallel to 食事に招く 'invite to a meal'). The benefactive ~てくれる frames the invitation as a kindness done for the speaker.