Structure
As is standard for Classical/Romantic-era concertos, the work is in three movements:
I. Allegro con brio
II. Largo
III. Rondo. Allegro
Allegro con brio
This movement is known to make forceful use of the theme (direct and indirect) throughout.
[edit]Orchestral Exposition
In the orchestral exposition, the theme is introduced by the strings, and used throughout the movement. It is developed several times. In the third section (second subject), the clarinet introduces the second main theme, which is in the relative major key, E flat major.
Second exposition
The piano enters with an ascending scale motif. The structure of the exposition in the piano solo is similar to that of the orchestral exposition.
Development
The piano enters, playing similar scales used in the beginning of the second exposition, this time in D major than c minor. The music is generally quiet.
[edit]Recapitulation
The orchestra restates the theme in fortissimo, with the wind instruments responding by building up a minor 9th chord as in the exposition. For the return of the second subject, Beethoven modulates to the tonic major, C major. A dark transition to the cadenza occurs, immediately switching from C Major to C Minor.
Cadenza
Beethoven wrote one cadenza for this movement. The cadenza Beethoven wrote is at times stormy and ends on a series of trills that calm down to pianissimo.
Coda
Beethoven subverts the expectation of a return to the tonic at the end of the cadenza by prolonging the final trill and eventually arriving on a dominant seventh. The piano plays a series of arpeggios before the music settles into the home key of C minor. Then the music intensifies before a full tutti occurs, followed by the piano playing descending arpeggios, the ascending scale from the second exposition, and finally a resolute ending on C.. Largo
The second movement, which is in E major, opens with the solo piano. The opening is marked with detailed pedalling instructions. Rondo – Allegro
The finale is in a sonata-rondo form. The movement begins in C minor with an agitated theme played only by the piano. The movement ends with a C major coda marked presto. (Wikipedia)

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