Arthur Stewart (Art) Farmer (August 21, 1928- October 4, 1999), was an American jazz trumpeter and flugelhorn player. He also played flumpet, a trumpet/flugelhorn combination designed for him by David Monette .

From 1945 to 1959 he played in several important bands, including those of Benny Carter, Wardell Gray, Gigi Gryce , Lionel Hampton, Jay McShann, Gerry Mulligan, Johnny Otis, and Horace Silver. He and Benny Golson led the Jazztet from 1959 to 1962, after which he formed a group with Jim Hall. In 1968 he joined the Austrian Radio Orchestra and lived and toured in Europe for several years.

Farmer also recorded extensively as a leader throughout his later career.