1. Allegro con brio: This is the first movement and is in sonata-allegro form. It begins with a lively and energetic theme in the piano, followed by the cello presenting a second, more lyrical theme. The development section is extensive, and the recapitulation brings back both themes in an exciting and triumphant manner.
2. Adagio con variazioni: This is the second movement and consists of a theme and five variations. The theme is a simple and beautiful melody introduced by the cello, and each variation explores different aspects of the theme. The variations display Beethoven's mastery of counterpoint, harmony, and melodic invention.
3. Allegro: The third movement is a scherzo, and it provides contrast to the slower and more lyrical second movement. It is in a triple meter and has a playful and energetic character. The middle section features a contrasting trio section in a contrasting key.
4. Allegro: This is the fourth and final movement. It is in rondo form, with a main theme that alternates with contrasting episodes. The main theme is energetic and driving, while the episodes provide moments of contrast and lyrical expression. The movement ends with a brilliant and virtuosic coda.
Overall, the Sonata for Cello and Piano in D Major is a significant and beloved work in the cello repertoire. It showcases Beethoven's genius in melody, harmony, and formal structure and is considered one of the greatest cello sonatas ever written.