The composer of the Enigma Variations is Edward Elgar, a British composer who lived from 1857 to 1934. He was known for his compositions of orchestral music, chamber music, and choral works. His most famous work is the Enigma Variations, a set of 14 variations on an original theme. The variations were dedicated to his friends and acquaintances, and each variation was meant to represent a different person. The Enigma Variations remain one of Elgar's most popular works.