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Calder was born in Montreal, Canada, into the Calder family associated with the brewing industry in Alloa, Scotland, and spent his childhood in Kinross, and studied at Bishop's College School in Sherbrooke before studying economics in Zurich, Switzerland, in the late 1940s.
Calder was a friend of Samuel Beckett, becoming the main publisher of his prose-texts in Britain after the success of Waiting for Godot on the London stage in 1955–56. During the 1950s, Calder published the translated work of Anton Chekhov, Leo Tolstoy, Fyodor Dostoevsky, Goethe and Zola, including most of the work of April FitzLyon, and was the first publisher to make William S. Burroughs available in the United Kingdom.
From 1963 to 1975, Calder was in partnership with Marion Boyars, and the company was known as Calder and Boyars. The championing of freedom of speech led to Calder's involvement in a number of prosecutions for obscenity, including one in 1966 for publishing Hubert Selby Jr's Last Exit to Brooklyn. While the initial trial resulted in a guilty verdict, the case was won on appeal, and effectively ended literary censorship in Britain.
The imprint continues to publish Howard Barker, Tim Waterstone, and other figures of literature both past and present. In 2002, John Calder opened The Calder Bookshop Theatre at 51 The Cut, Waterloo, London. To celebrate his fifty years in publishing, the arts and politics a festschrift  was produced. During 2006, Lou MacLoughlan and Louise Milne produced the documentary John Calder: A Life in Publishing commemorating his life.
In April 2007, Calder sold his business to independent publishers Alma Books/Oneworld Classics; the imprint retained his name, while the rights to the non-theatrical work of Beckett were acquired by Faber.
Calder was a co-founder of the Traverse Theatre in Edinburgh. He was also responsible, along with Sonia Orwell and Jim Haynes, for devising and co-creating an International Writers' Conference held at the Edinburgh International Festival in 1962 and then a Drama Conference with Kenneth Tynan in 1963. These innovative events, intended to draw together writers from all over the world, were arguably a forerunner of the Edinburgh Book Festival, which was not founded for another twenty years. The experience of this first conference was revisited at a Book Festival discussion during the 2012 Edinburgh International Festival.
John Calder also led a hectic life outside publishing. He was a major investor in the Partisan Coffee House, a radical New Left venue in Soho. In 1970, he stood for election as a Scottish Liberal Party candidate for Kinross and Western Perthshire, finishing 4th.
However, he was otherwise mainly known for his interests in the arts in general and his passion for opera in particular. In 1963 he founded and ran for some ten years Ledlanet Nights, a general festival of the arts, held in the hall of his then home, a baronial house at Ledlanet near Milnathort.
Calder was married to Christya Myling from 1954 to 1961. They have a daughter named Jamie (b. 1954). Calder and Bettina Jonic were married in 1961. That lasted until 1975, and produced another daughter, Anastasia (b. 1963). Calder married Sheila Colvin, who had been a friend and partner from his earliest involvement with the arts, and the Traverse Theatre in Edinburgh. She is a former associate director of the Edinburgh International Festival and director of the Aldeburgh Festival. The couple lived in Edinburgh and Paris.
- O'Mahony, John (20 July 2002). "The Profile: John Calder". The Guardian. London.
- The Guardian 20 Jul 2002 Page 72
- McMillan, Joyce (12 April 2014). "The Traverse celebrates John Calder's legacy". The Scotsman. Retrieved 15 August 2018.
- Ian Miller, Other lives: Neville Armstrong, The Guardian, 26 September 2008, accessed 27 July 2021
- Steven, Alasdair (15 August 2018). "Obituary - John Calder, ground-breaking publisher, co-founder of the Traverse and leading figure at the Edinburgh festival". Glasgow Herald. Retrieved 15 August 2018.
- Fisher, Mark (27 March 2014). "Interview: John Calder, 'the most important English-language publisher of the 20th century'". The List. Retrieved 15 August 2018.
- Owen, Peter (2 February 1999). "Marion Boyars obituary: Pioneer publisher of the avant-garde". The Guardian. Retrieved 15 August 2018.
- Lawless, Jill. "John Calder, British publisher and champion of avant-garde, dies at 91". Washington Post. Retrieved 18 August 2018.
- Hodgkinson, Will (16 October 2004). "Culture quake: Last Exit to Brooklyn". The Daily Telegraph. Retrieved 6 March 2018.
- Morin, Carole (2001). Penniless in Park Lane. London: John Calder Publishers. p. 143. ISBN 0-7145-4314-4.
- - The Calder Bookshop Theatre
- "In Defence of Literature: for John Calder - Fifty years of publishing literature, politics and the arts". Mosaic Press. Retrieved 24 April 2011.
- Rickett, Joel (21 April 2007), "The bookseller", The Guardian. Retrieved 1 July 2007.
- Demarco, Richard (September 2018). "John Calder: Edinburgh Iconoclast". artWORK. p. 3.
- Bartie, Angela and Bell, Eleanor (2012), The International Writers' Conference Revisited: Edinburgh 1962, Cargo Publishing.
- O'Mahoney, John (19 July 2002). "Publishing's one-man band". The Guardian.
- Bishopsgate Institute Podcast: The Partisan Coffee House: Cultural Politics and the New Left. Mike Berlin, 11 June 2009
- Morton, Brian (3 March 2017). "Happy Days". Scottish Review of Books. Retrieved 15 August 2018.
- Calder, John (2001). Pursuit: the Uncensored Memoirs of John Calder. London: John Calder Publishers. p. 619. ISBN 0-7145-4313-6.
- Calder, John (2002). The Philosophy of Samuel Beckett. Calder Publications Ltd. ISBN 978-0-7145-4283-6.
- Calder Publications - archived version of website as it was on 23 May 2002.
- Calder and Boyars Manuscripts - Lilly Library Manuscript Collections, Indiana University
- Louise Jury, "Publish and be damned: A defender of free speech" – a profile of John Calder, The Independent on Sunday, 21 March 2007.
- Tom Tivnan, "I am Legend", a feature on John Calder on his sixtieth anniversary in publishing, The Bookseller, 30 January 2009.