This music is composed by Pyotr Ilyich TchaikovskyRelative level of fame is: 60593
Oops... Its not a mistake!
The original name of this music is "Act IV. No. 27 Dance of the Little Swans: Moderato"
But all over the world "Allegro moderato" (from Act II, No. 13 Dances of the Swans) is known as the "Dance of the Little Swans".
https://en.wikipedia.org/wiki/Swan_Lake