As far as anyone can tell, this is the first of Haydn's assays into four-movement structure in the piano sonatas. (It wasn't a form he was going to be sustaining, however; most of the sonatas are in three movements.)
First Movement: Allegro
The sonata form of the early Classical period is slightly different from its later incarnation. In particular, the secondary theme tends to come quite early in the movement (here, in measure 5!) immediately following what has been dubbed a bifocal close. Instead of an actual modulation to the secondary key, a half-cadence in the tonic key is immediately followed by an abrupt change of key into the dominant key. As a result, the secondary key remains somewhat unstable, and is not usually confirmed until later on in the movement -- as in this case, with the closing theme which is first heard at measure 13.
The bifocal close creates a problem during the Recapitulation -- the very ease of reaching the secondary theme (now in the tonic key, immediately following a half-cadence) tends to render the latter part of the movement dangerously predictable. Skilled composers such as Haydn used a great variety of techniques to avoid that predictability and thus to retain the listener's attention. In this sonata, Haydn avoids beginning the Recapitulation with the primary theme at all: the recapitulation begins with the secondary theme, and so the entire problem is cleverly side-stepped. (Beginning with a secondary theme creates what is sometimes called a "binary" sonata form, a poorly-chosen term but unfortunately well-established.)
Second Movement: Minuet
A fine, clearly Galant-inspired minuet movement with a Trio that seems charged with the spirit of the Empfindsamkeit, or concentrated emotional world, of composers such as C.P.E. Bach.
Third Movement: Adagio
The lovely minor-key adagio, in a binary form, is not only reminiscent of Haydn's slow-movement symphonic forms, but also owes a clear debt to aria forms of the period. Both halves of the binary form contain short improvised cadenzas. A. Peter Brown has pointed out that this movement shows a clear debt to the keyboard concertos of Georg Reutter, Haydn's erstwhile teacher at St. Stephen's during the 1740s. The similarity between this movement and the second movement of Reutter's Concerto in C Major is quite compelling; in the following example, the Reutter is the topmost grand staff, transposed in to G Minor for purposes of comparison:
Fourth Movement: Allegro molto
Another high-spirited romp in 3/8 time, typical of this era. However, this particular movement refers back to the first movement in its use of another bifocal close in the Exposition, with an interesting 'feint' by Haydn during the Recapitulation to avoid predictability. In this case, Haydn shortens the Recapitulation's primary theme by just enough to create a jarringly irregular phrase -- it always sounds as though the performer had a brief memory lapse. The sudden surprise is more than enough to keep the listener from assuming he or she can predict what's coming up next.