"The RSC realised his pioneering vision of a resident ensemble of actors, directors and designers producing both classic and modern texts with a clear house style in both Stratford and London", the National Theatre said. His career highlights include staging the English-language premiere of Samuel Beckett's Waiting for Godot and the world premiere of Harold Pinter's Homecoming, as well as adaptations of Shakespeare's Antony and Cleopatra, which starred Judi Dench and Anthony Hopkins, The Merchant of Venice, with Dustin Hoffman, and As You Like It, with his daughter, Frost/Nixon actress Rebecca Hall.
Gregory Doran, artistic director of the Royal Shakespeare Company, said: "Sitting at the same desk Sir Peter used at Stratford, I feel like a petty man compared to his extraordinary achievements".
Sir Peter Hall on the terrace of the National Theatre, London with Laurence Oliver.
Peter Hall was a force of nature whose impact, not merely on the stage, but on the entire panoply of national cultural life, was formidable and far-reaching.
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Sir David said in a statement that "every living playwright owes him a debt".
Trevor Nunn, who was director at the National from 1997 to 2003, said that Hall's greatness lay in his "astonishing originality, his unparalleled daring, his profound scholarship, his matchless articulacy and his visionary understanding of what we call "the theatre" could be".
'Our honest thoughts and sympathies are with Sir Peter's family and friends at this sad time'.
'Not only was he a great director of theatre and opera, he was a politician who fought for the Arts. "He was - and is - the godfather (in both senses) of British theatre and like countless directors, writers and actors of several generations I have much to be grateful to him for".
Leaders at the National, where Hall was director from 1973 to 1988, also paid tribute. "A great director and shaper of British theatre".
Sir Peter Hall's production of Britten's A Midsummer Night's Dream was revived at the 2016 Glyndebourne Festival.
The director, who founded the Peter Hall Company, was married four times.