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Mugler, known for his daring theatrical designs featuring broad shoulders and plunging necklines, dressed the likes of Beyonce, Lady Gaga, David Bowie and Duran Duran - among many others - during his career at the top of the fashion industry.
"I am deeply sad to hear that yet another of fashion’s great innovators has left our world this week. Thierry Mugler, literally shaped the 1970s and 80s with his spectacular sharp designs," wrote Nick Rhodes on Duran Duran's Facebook page.
Born Manfred Thierry Mugler in 1948, the designer had an interest in making his own clothes.
He went on to open his first boutique in Paris during the 1970s.
Mugler became known for his designs featuring plunged necklines and constricted waists.
He appeared to retire from fashion in the early 2000s, choosing to create one off pieces for Lady Gaga and costumes for Beyoncé.