This delightful piece by Beethoven is very popular. While the composer's original piece was for piano solo, this arrangement is for Violin and Piano. Here are the parts which you can download and print: Violin part and Score (which also serves as the piano part). See the left hand menu for alternative arrangements for different instruments.
This piece is classified as one of the composer's Bagatelles (no. 25) though it wasn't published during his lifetime. The latest theory is that Elise was Elisabeth Rockel who was a close friend of the composer. For other shorter Piano pieces by Beethoven try Bagatelles, Rondos and other Shorter Works for Piano from The Music Room (UK).