This is one of Balanchine’s very early works, first presented by Diaghilev’s Ballets Russes in Paris in 1928 to music (and a libretto) by Igor Stravinsky. Its first American production was with the American Ballet at the Metropolitan Opera House in 1937.
To the Greeks, Apollo represented many things, but for the purposes of this ballet, Stravinsky focused on Apollo the god associated with the arts and his relationship with the Muses. The Muses, for this story, were chosen by Stravinsky for their appropriateness for choreography. Stravinsky said, “Calliope personified poetry and its rhythm; Polyhymnia represents mime; Terpsichore, combining in herself both the rhythm and the eloquence of gesture, reveals dancing to the world and thus among the Muses takes the place of honor beside Apollo.”