The first sonata in A-minor is written in 1851. it consists of three movements with the first being a very dramatic work, the second a wonderfully melodic, with multiple sections, and the third a stormy movement with rumbling left-hand broken octaves that reminds us of, for example, the last movement of Beethoven's seventh sonata or the Tarantella of the Kreutzer Sonata. It took Schumann only three days to complete the sonata.
The difference that stands out the most is that the instruments, though both have much solistic material, are intensified as a chamber instrument. The virtuosity, especially in the first movement of the piano part, and the delicacy that has to be maintained makes it a challenge to play. If we compare his writing style with the composers from the classic-era, we can see that the violin has a more dominant line with the melodic lines and in the same time an intensified part for the piano. Also the way of writing in the piano gives many more opportunities for the pianist to play with the pedal and create different atmospheres.
When Clara and Joachim performed the piece in May of 1853, Clara noted about the beauty of Joachim's playing that: "Only then did I fully understand the work'. (Great masters of the violin, Boris Schwarz, P.265)
The first movement of this sonata is written in a dramatic style in the low register of the violin (g-string). Above the piece, it states 'Mit leidenschaftlichem Ausdruck' which means 'with passionate expression'. The piano part, in general, is played with an intricate accompaniment and thematic material. Making it technically sometimes to keep the theme and the dramatism at the same time. Especially in the development section of this movement we see a very different technical style of writing than in the violin-piano works from before. The coda, which starts with the broken octaves in the right hand of the piano and the main theme in the violin part, brings us to a great climax that is especially made by the violin.
The second movement, which is a very free and joyous Allegretto in F major, brings out a very different style of Schumann's composing. Even though the period in which he wrote this sonata was a dramatic and difficult one for him, he wrote this in a rather happy mood. Only the gorgeous minor part in the middle of this movement hints towards the mental state that he was in.
The third movement goes back to the a-minor and is the most turbulent of all the movement. The broken octaves in the left hand of the piano, that he used previously in the first movement right hand, is of a very different character. This piece should be more precise in metre than the first movement because the dramatism comes more from the conversation of the instruments rather than the freedom in rhythm, like in the first movement. The biggest change in character in this movement comes when the piano and violin go to E major in the middle part and the precise sixteenth accompaniment of the piano becomes triplets. This part definitely brings a big contrast to the steady rhythmical pattern from before. In the coda of this movement, we see the theme of the first movement, which is now written in the sixth degree (F) instead of tonic (a). The hint is short and soon we are back in the motives of the third movement which brings us to a great passionate end of the sonata.