The play written by JK Rowling won nine awards including for best new play.
Harry Potter and the Cursed Child emerged as a big winner at the 2017 Olivier Awards, with wins in nine categories.
The two-part play - a follow-up to JK Rowling's Harry Potter series of books - won in nine of the 11 categories it was nominated in at the ceremony at London's Royal Albert Hall.
Cursed Child won Best New Play, Best Actor (Jamie Parker), Best Actor in a Supporting Role (Anthony Boyle), Best Actress in a Supporting Role (Noma Dumezweni) and Best Director (John Tiffany).
It also won in the Best Lighting Design, Best Costume Design, Best Sound Design and Best Set Design categories.
Kenneth Branagh won the Special Award, for his outstanding contribution to British theatre and gave an inspiring speech in which he encouraged people to keep dreaming.
"People sometimes ask me how I do it, and here's the answer - we do it. I was inspired to dream and my advice to everyone is: dream big. There are no mistakes only lessons.
"We can help to change the world just a little bit. I've seen the evidence. Shakespeare was right: we are such stuff that dreams are made of. Keep making stuff keep dreaming," Branagh said.
Actress Judi Dench praised the actor-director saying, "I am so glad you are getting this award. And please employ me again'', while Mark Rylance introduced the actor and director with the words: ''He makes it seem as easy. I know he has grave doubts, full of fears like any of us, and yet he turns up."
Other winners included Billie Piper for Best Actress for her role in Yerma, which also won Best Revival.
Groundhog Day won Best New Musical and Best Actor in a Musical for Andy Karl, while Glee actress Amber Riley won Best Actress in a Musical for Dreamgirls.
Presenters at the ceremony included Lin-Manuel Miranda, John Boyega, Nathan Lane, Denise Gough, Andrew Garfield and Maureen Lipman.
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