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Breathnach grew up in the Liberties of Dublin, where his father was a silk weaver. His uncle Joe was a player of the uileann pipes and a member of the Piper's Club. He started learning the pipes from John Potts of Wexford and William Andrews, then with the renowned piper Leo Rowsome.
In the 1950s he decided to publish some of his music collection. Tunes were contributed by pipers such as his uncle Joe, John Potts, Tommy Reck, Matt Kiernan and Willie Clancy, fiddlers such as John Kelly, Donncha Ó Cróinín, Tommy Potts and Tom Mulligan, flutists and whistlers such as John Egan, John Brennan and Michael Tubridy, and box-player Sonny Brogan. The collection was called Ceol Rince na hÉireann (dance music of Ireland).
The first volume of his music collection was published in 1963. A second volume appeared, to great acclaim, in 1976. This included music from, amongst others, James McEnery (Limerick), John Doherty (Donegal), Micho Russell (Clare) and Denis Murphy (Kerry). Additional volumes based on his work were published in 1985, 1996 and 1999.
By the time of his death he had collected over 7,000 tunes. His efforts were responsible for saving numerous tunes and he is generally recognised as a major figure in the preservation and continuation of traditional Irish music.
- "Willie Clancy the man and his music"', Ceol; 2/3 (1965) 70-77
- Ceol Rince na hÉireann, vol. 1 (1963), vol. 2 (1976), vol. 3 (1985)
- Folk Music and Dances of Ireland (1971) ISBN 1-900428-65-2
- "Tribute to Seamus Ennis", Musical Traditions No. 1, 1983 
- Irish Times interview with Fionnuala Mulcahy 1984
- Ó Canainn, Tomás, Traditional Music in Ireland, Routledge & Kegan Paul, 1978, ISBN 0-7100-0021-9.
- Ó Riada, Seán, Our Musical Heritage, The Dolmen Press, 1982, ISBN 0-85105-389-0.
- Vallely, Fintan (1999), The Companion to Irish Traditional Music, New York University Press. ISBN 0-8147-8802-5.
- Irish Music Centre, Boston College