The first movement is in standard concerto form, with orchestral ritornelli bracketing several solo sections, the first of which moves from D minor to its relative major key of F, and the second of which cycles through other keys to return to D minor and recapitulates the exposition entirely in D minor, like classical sonata form. There is also a cadenza at the end of the movement in the middle of the final ritornello, as is usual in classical concerti.
The second movement is a five-part rondo (ABACA), with the A sections all in the tonic of B-flat major, the B section moving to the dominant, F major, and the C section in the relative minor, G minor.
The third movement, despite being titled a "rondo," is really much closer to sonata form, with an exposition moving from D minor to F major, a development that starts in D minor (its main concession to rondo form) and goes through other keys before returning to the tonic, and a recapitulation that plays in D minor everything previously exposed in F major. There is then a cadenza and a dramatic pause, and then a big, jubilant coda entirely in D major to end things happily.
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Composed by Mozart.
I'm not sure what you mean... The form of the sonata is sonata form. Or if you want to get fancy, it's First Movement Sonata-Allegro Form.
Depending on where you are from, the most popular songs by Mozart in America are; the first movement of Eine Kleine Nachtmusik, Symphony No. 40, Piano Concerto No. 21, and Piano Sonata in A Major K. 331.
Mozart's works were catalogued by Kochel. The K number comes from his name. Sometimes KV is used as "Kochel Verz".
Sonata K. 120 & K. 141 are known as some of the most difficult ones. I've played them before and they are very confusing.