Violin Concerto in D major, Op. 77 is one of the best-known of all violin concertos.
It follows the standard concerto form, with three movements in the pattern quick-slow-quick:
Allegro non troppo (D major)
Adagio (F major)
Allegro giocoso, ma non troppo vivace - Poco piu presto (D major)
Originally, however, the work was planned in four movements like the second piano concerto. The middle movements, one of which was intended to be a scherzo, were replaced with what Brahms called a "feeble Adagio."
The work was written in 1878 for the violinist and friend of Brahms, Joseph Joachim, who was the dedicatee. Brahms asked Joachim's advice on the writing of the solo violin part. The most familiar cadenzas used in the work are by Joachim, though a number of people have provided alternatives, including Leopold Auer, Max Reger, Fritz Kreisler, Jascha Heifetz, George Enescu, Nigel Kennedy and Rachel Barton Pine. A recording of the concerto released by Ruggiero Ricci has been coupled with sixteen different cadenzas.
The work was premiered by Joachim in Leipzig on January 1, 1879. Various modifications were made between then and the work's publication by Fritz Simrock later in the year.
Source: Wikipedia