Theme of Aya - This is the protagonist's theme song.
Eva's Aria - This is Eve's haunting opera aria, also titled "Se Il Mio Amore Sta Vincino." Lyrics are available.
Primal Eyes - The intro song of the game.
Arise Within You - An upbeat song, this is the battle theme of Parasite Eve, one of the best battle themes there are.
Matrix - Dude, all I know right now is that it has nothing to do with Keanu Reeves.