Although not really typical of his output, this flowing piano piece by Beethoven (which translates as "for Elise") is very well-known. Although it wanders off into strange territory, it invariably returns to the main theme, anticipating each return with a playful hovering around the note of E. We also have arrangements of Fur Elise for these instruments: Flute, Oboe, Clarinet, Soprano Sax, Tenor Sax, Trumpet, Violin and Viola all including piano accompaniment. Note that some editions have an "E" in the 2nd half of bar 8 but we have a "D" in this position, as this option seems to be slightly more common in printed editions and in performance.
Although Für Elise wasn't published during Beethoven's lifetime but 40 years after his death it has become one of his most popular piano works, in part because it is a shorter work and easier than much of his piano music. For publication purposes this piece has been classified as one of the composer's Bagatelles (no. 25), but it is the form of a Rondo (A-B-A-C-A with the A section being the main theme to which the piece returns). 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). You can see a piano roll animation of "Für Elise" in the video below, while below that you can play the mp3 file and see the sheet music before downloading.