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Back in Warsaw that year, Chopin heard Niccolò Paganini play the violin, and composed a set of variations, Souvenir de Paganini. It may have been this experience which encouraged him to commence writing his first Études, (1829–32), exploring the capacities of his own instrument. On 11 August, three weeks after completing his studies at the Warsaw Conservatory, he made his debut in Vienna. He gave two piano concerts and received many favourable reviews—in addition to some commenting (in Chopin's own words) that he was "too delicate for those accustomed to the piano-bashing of local artists". In one of these concerts, he premiered his Variations on Là ci darem la mano, Op. 2 (variations on an aria from Mozart's opera Don Giovanni) for piano and orchestra. He returned to Warsaw in September 1829, where he premiered his Piano Concerto No. 2 in F minor, Op. 21 on 17 March 1830.

Where did Chopin debut after completing his studies?
Vienna