Beethoven's legendary final piano sonata ( No. 32 in C Minor, Op. 111) has only 2 movements. The 1st is fast and fiery (you can hear it here), in some ways recalling the famous "Pathetique" Sonata, also in C Minor.

The 2nd movement, which you see in the video/analysis above, is completely different - a lengthy, meandering set of variations on a radiant, simple theme in C Major. The movement can last anywhere from 15-20 minutes.

The first 3 variations are fairly straightforward in structure,with the note values increasing in value up through the crazy "boogie-woogie" Variation #3. With Variation #4, the accompanying notes continue to be densely fast, but the mood changes and from there to the end, the variation structure is freer. (The sections marked "Trills" and "Interlude" might be thought of as a fantasia-like variation, but I hear them more as a development-like departure from the thematic structure, which returns in the recapitulation-like Variation #5.)

Note the use of dramatic trills at the end of Variation 4 and at the beginning of the incomplete 6th variation. Also, note that by dispensing with the 2nd half of the tune (which always begins in minor), the final variation achieves a kind of closure by remaining suspended in C Major.