That would be the great Howard Shore.
The music of the The Lord of the Rings film trilogy was composed, orchestrated, conducted and produced by Howard Shore. Shore wrote many hours of music for The Lord of the Rings, 10 hours of which have been released in The Complete Recordings CD/DVD boxed sets.
Howard Shore composed music for LOTR triology
A.R. Rahman did not compose any music for any of the Lord of the Rings films.
Howard Shore - http://www.imdb.com/name/nm0006290/
Music of The Lord of the Rings film trilogy was created on 2003-11-25.
There are many online resources one can use to find the music to the Lord of the Rings theme. YouTube has many videos with music from Lord of the Rings. On Last Fm and Music of LOTR websites, both have music from the popular movie available.
There are many books dedicated to sheet music for the Lord of the Rings. You can find these at any of your local music stores.
Lord of the Rings is not the name of a song, there are many pieces of music in the movies.
Howard Shore was responsible for 'additional music'. Soundtrack listing courtesy of IMDb; * "Flaming Red Hair" Music Composed & Performed by David Donaldson / David Long / Steve Roche (as Stephen Roche) / Janet Roddick with Peter Daly / Chris O'Connor / Ruairidh Morrison / Grant Shearer Courtesy of Mana Music * "In Dreams" Written by Fran Walsh and Howard Shore Performed by Edward Ross Courtesy of Reprise Records * "May It Be" Composed & Performed by Enya Played during the end credits * "Aníron" Composed & Performed by Enya
Music Inspired by The Lord of the Rings - Mostly Autumn album - was created in 2001-11.
Howard Shore
The soundtrack was composed by Howard Shore.