It's sectional variation time!
These variations are large structures and that is true for this piece in A flat. The theme is in a rounded binary form and it is varied five times.
The A section of the theme is an 8 measure contrasting period. The first cadence in the fourth bar is a half cadence and the second cadence in the eighth measure is a PAC in the dominant key of E flat. This eight measure period is then basically repeated though there are some fairly significant melodic alterations and a significant change to the PAC by taking away some of the blurring of the PAC that occurs the first time through. The B section is a ten bar parallel period with a weak half cadence in Eb in the fourth bar and a PAC in E flat the eighth measure and a cadential extension to the tenth bar. That tenth bar then modulates back to the key of A flat and leads to a full repitition of the A section like it was the second time in the beginning.
The first variation keeps the same harmonic structure but there are a few changes to the music. One of the major changes is the thirty second note rhythmic pattern that is very prevalent in the melody part. The accompaniment which often echoed the melody an octave lower during the theme takes a much more minor role just playing chords on downbeats. The cool thing about this variation is in the B section where Beethoven has a cool ascending scalar line in the melody doing three three thirty second notes in two different octaves that rise.
The second variation is extremely FUN! The harmonies are once again are the same but the entire variation is a boom-chick thirty second note pattern that outlines the chords. The bass line is mostly in octaves and mostly has the melody on the boom while the treble clef part does the chicks. Very cool.
The third variation has a similar boom chick between the treble and bass parts but by switching the rhythm to sixteenth notes and moving to minor mode (A flat minor = 7 flats, ahhh!) the piece takes a much more somber tone in this variation and the rising line in the upper voice is very poignant. There is a more melodic break during the B section of this variation.
I would call the fourth variation the "waltz" variation due to the bass part having stacatto notes first on one and three (time sig is 3/8 if I haven't mentioned it yet) then on one and three and the and of three and then on all three beats. This section also has a very neat melody part, which is in octaves and also jumps octaves every couple of notes, giving a Bach like feel of two different melodies going on at the same time and a wonderful thirty second note descending run in one measure. It also returns back to the major key.
The last variation is the virtuosic section. The first time through the A section is dominated by the sixteenth triplet rhythm in both hands and the second time through quickens to mostly thirty second notes in both hands creating a very dense texture. The B section has much the same texture. The return to the A section however lightens up to a point that hasn't been heard since the first variation, which helps to signal the piece is coming to an end. The fastest rhythm is sixteenth notes that are only in one voice while the other voices stick with eighth notes.
The last eight measures of the piece serve a termanitive function with the harmony not straying from I and V and a no melody just a little chromatic line in the soprano.