Jude Law learned to play the saxophone and Matt Damon learned to play the piano for this film. However while Damon's training enabled him to recreate the proper keyboard fingering, the music heard in the film is played by Sally Heath (the Bach) and Gabriel Yared (the Vivaldi).
Anthony Minghella originally wanted Tom Cruise for the role of Ripley but after seeing Good Will Hunting (1997), he decided to cast Matt Damon.