This music is composed by Pyotr Ilyich Tchaikovsky
Relative level of fame is: 63428
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".