In 1862, Brahms moved his primary residence to Vienna. Here, he was completely captivated by the virtuosity of the renowned pianist Carl Tausig (1841–1871), whom he met there. Although their personalities were almost diametrically opposed to Brahms's own, the two quickly became close and enjoyed performing and discussing music together.

Brahms, observing the precedents set by Schumann's Opp. 3 and 10, and Liszt's Études d'exécution transcendante d'après Paganini, had also considered composing similar études himself. It was then that Tausig proposed to Brahms the idea of composing a brilliant set of variations on a Paganini theme, which became the impetus for the composition.

This set of variations, Op. 35, consists of two books, each containing 14 variations, totaling 28 variations. Each variation successively presents new technical challenges, making them études of extreme difficulty. Brahms inscribed the work with the title "Studies for the Piano: Elaborate Exercises for the Fingers." The theme for both books is taken from Paganini's Caprice No. 24 in A minor for solo violin.

When Liszt's pupil, Moriz Rosenthal, began performing this work, Liszt reportedly said, "This piece by Brahms is better than mine." However, he did not forget to add, "But mine was composed more than ten years earlier."

Furthermore, when Rosenthal asked Brahms whether all 28 pieces should be performed consecutively, Brahms reportedly joked, "You may take a rest after the first book. But if the audience is still not satisfied, then you may proceed to the second book."

The premiere was given by Brahms himself in Zurich in November 1865, and Tausig performed it in Berlin in March 1867. The work is dedicated to Brahms's pupil, Elisabeth Stockhausen.