This is probably one of the best known piano solos of all time. It was written on 27th April 1810 in Beethoven's 40th year. It was written when Beethoven was profoundly deaf. Six years later he would be totally deaf.
I included it in my twelve pieces because just about every new pupil I have ever met has wanted to play it. The thing is that the only really know of the main melody. This is the whole thing.