Paul William Rutherford (29 February 1940 – 5 August 2007) was an English free improvising trombonist.
Born in Greenwich, South East London, Rutherford initially played saxophone but switched to trombone. During the 1960s, he taught at the Guildhall School of Music and Drama.
In 1970, Rutherford, guitarist Derek Bailey and bassist Barry Guy formed the improvising group Iskra 1903, which lasted until 1973. (This formation was documented on a double-LP from Incus, later reissued with much bonus material on the 3-CD set Chapter One (Emanem, 2000). A film soundtrack was separately released as Buzz Soundtrack.) Iskra 1903 was one of the earliest free improvising groups to omit a drummer/percussionist, permitting the players to explore a range of textures and dynamics which set it apart from other contemporary improvising ensembles like SME and AMM. The group's unusual name means "spark" in Russian; it was the title of a revolutionary newspaper edited by Lenin. The "1903" designation means "20th century music for trio"; occasionally Evan Parker played with the group (Iskra 1904) and Rutherford also at one point assembled a 12-piece ensemble called, inevitably, Iskra 1912.