Edward Elgar composed his Variations on an Original Theme, Op. 36, popularly known as the Enigma Variations, between October 1898 and February 1899. It is an orchestral work comprising fourteen variations on an original theme.

Elgar dedicated the work "to my friends pictured within", each variation being a musical sketch of one of his circle of close acquaintances (see musical cryptogram). Those portrayed include Elgar's wife Alice, his friend and publisher Augustus J. Jaeger and Elgar himself.

In naming his theme "Enigma" Elgar posed a challenge which has generated much speculation but has never been conclusively answered. The Enigma is widely believed to involve a hidden melody.

The name of the variation IX (NIMROD) refers to Augustus J. Jaeger, who was employed as music editor by the London publisher Novello & Co. He was a close friend of Elgar's, giving him useful advice but also severe criticism, something Elgar greatly appreciated. Elgar later related how Jaeger had encouraged him as an artist and had stimulated him to continue composing despite setbacks. Nimrod is described in the Old Testament as "a mighty hunter before the Lord", Jäger being German for hunter.

In 1904 Elgar told Dora Penny ("Dorabella") that this variation is not really a portrait, but "the story of something that happened". Once, when Elgar had been very depressed and was about to give it all up and write no more music, Jaeger had visited him and encouraged him to continue composing. He referred to Ludwig van Beethoven, who had a lot of worries, but wrote more and more beautiful music. "And that is what you must do", Jaeger said, and he sang the theme of the second movement of Beethoven's Piano Sonata No. 8 Pathétique. Elgar disclosed to Dora that the opening bars of "Nimrod" were made to suggest that theme. "Can't you hear it at the beginning? Only a hint, not a quotation."

This variation has become popular in its own right and is sometimes used at British funerals, memorial services, and other solemn occasions. It is always played at the Cenotaph, Whitehall in London at the National Service of Remembrance. A version was also played during the Hong Kong handover ceremony in 1997 and at the opening ceremony of the London 2012 Olympic Games. The ?Nimrod? variation was the final orchestral composition (before the national anthem) played by the Greek National Orchestra in a televised June 2013 concert, before the 75-year-old Athenian ensemble was dissolved in the wake of severe government cutbacks.

An adaptation of the piece appears at the ending of the 2017 film Dunkirk as part of the score

'You were often on my mind when I was writing', wrote Robert Schumann to Joseph Joachim who had encouraged him to write this concerto. In view of Schumann's illness, however, Joachim began to have his doubts about the value of the work. In his will, Joachim prohibited the first performance until the 100th anniversary of Schumann's death in 1956. After detailed editorial work, the premiere was brought forward to 1937.

The theme of the middle movement probably formed the basis of Schumann's Geistervariationen ('Ghost Variations'), the character of the third movement is that of a grand polonaise. Yehudi Menuhin who performed the world premiere of the unedited version of Schumann's solo part saw in this piece 'the bridge between Beethoven's and Brahms' concertos'.