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The LiederNet Archive: According to thewebsite "The LiederNet Archive is the world's largest reference archive of texts and translations of art songs and choral works." Search by composer, first line, title, or poet.
The Aria Database provides texts and translations for more than 1,200 operatic arias as well as a substantial collection of MIDI files of arias and ensemble numbers. Search by title, opera, composer, or character name.
An excellent website for Russian art song (including translations and IPA for fee plus free access to audio files of historic recordings from Russia) is here. FEE BASED!
Liner notes accompanying streaming sound and visual recordings may contain texts and translations. See the music subject resources list for access to databases like Naxos Music Library, the Database of Recorded American Music and Met Opera on Demand.
Books and e-books:
Books of translations are classified as ML54.6 in both the Reference Room and circulating stacks.
Librettos of texts of operas are listed in the online catalog under the name of the opera and librettist.
The following is available in the Music Library Reference section AND as an e-book: