His death was announced in a statement given to the BBC by his publisher, MacMillan.
"Colin was an author who inspired all those who worked with him", said Maria Rejt, his most recent editor. Dexter's writing also spawned spin-off TV shows, Lewis and Endeavour. His Morse - a cerebral curmudgeon with a love of ale and crossword puzzles - is an iconic character in mystery fiction. His first, Last Bus to Woodstock, was published in 1975 and written while the author was on holiday in Wales. "His was the sharpest mind and the biggest heart, and his wonderful novels and stories will remain a testament to both".
His series of 14 novels about the cynical crossword-loving detective and his loyal sidekick Sergeant Lewis received critical acclaim and was adapted into a long-running ITV series starring John Thaw as Morse.
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As well as making appearances in Morse, Dexter would also regularly pop up in episodes of Endeavour, which stars Shaun Evans as a young Morse in the early days of his career as a detective constable in Oxford.
MacMillan's publisher Jeremy Trevathan added that Dexter's death represented a "tectonic shift in the worldwide crime writing scene". He was one of those television characters who the nation took to their hearts.
Dexter was married to Dorothy with whom he had a son and daughter. "Very sad to hear of his death today".
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Norman Colin Dexter was born in 1930, in Stamford, Lincolnshire, and studied Classics at Cambridge University. Dexter's first story about the bad-tempered inspector was a hit and he went on to write thirteen more books featuring Morse and Lewis.
Dexter famously made cameos in nearly every episode of Inspector Morse.
Dexter was made an Officer of the Order of the British Empire for services to literature in 2000.
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