Who composed the music and who wrote the words to the opera Cosi Fan Tutti?

Wolfgang Amadeus Mozart composed the music and Lorenzo da Ponte was the librettist for the Opera Cosi fan tutte (note the spelling of the last Word :)

The title means something like "That's what they all do" where the "they" is feminine (that's why the Word needs the "e" ending rather than the "i", which would be masculine). Thus, "That's what all women do" :)