Schubert composed this work in late 1822, just after breaking off work on the Unfinished Symphony while sketching its incomplete scherzo. It was written for, and dedicated to, Carl Emanuel Liebenberg von Zsittin, who had studied piano with Johann Nepomuk Hummel, in the hope of some remuneration from the dedication.[2] It is not only a technically formidable challenge for the performer, but also a structurally formidable four-movement work combining theme-and-variations with sonata form. Each movement transitions into the next instead of ending with a final definitive cadence, and each starts with a variation of the opening phrase of his lied "Der Wanderer." The second movement, marked "adagio," states the theme in virtually the same way it is presented in the song, whereas the three fast movements begin with variants in diminution (that is, shortened note values): the first movement, "allegro con fuoco ma non troppo," a monothematic sonata form in which the second theme is another variant, the third, "presto," a scherzo in compound time, and the finale, marked simply "allegro," starting as a quasi-fugue and making increasing demands on the player's technical and interpretive powers as it storms on to its conclusion. (Wikipedi)