How much knowledge about Harry Potter's previous adventures does the Cursed Child require?

The stage play Harry Potter and the Cursed Child is apparently centred around the Harry Potter universe and while starting after his adventures in the primary book series seems to involve various ventures and references to past events, too.

I thus wonder, to which degree it can be enjoyed without too much of a thorough knowledge of the Harry Potter book series. Now, I would assume it won't bother much with reintroducing the whole universe and the major characters, so somewhat of a general knowledge of how the universe works and who is who seems to be required. But it's unclear to me how much of the actual plot from the book series or detailed historical background information about the universe is really required to understand and enjoy the play.

If that is too vague for you, let's get more specific by asking straight away if someone who has only seen the film adaptations of the book series will be able to thoroughly understand and enjoy the theatre play. Now, I'm sure there's various little references that one might not completely get, but is the primary story and the themes of the play still well-digestible for movie-only heretics?

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_{The answer to this question might naturally involve spoilers about the play. I personally don't care about them but for the courtesy of others reading this question, which is basically a pre-viewing question, you might want to consider hiding them behind spoiler-markup. But please make sure the answer still makes general sense without the spoiler blocks.}

Answer

Just the plot of the main series

Harry Potter and the Cursed Child makes frequent references to events and characters from the books. Having read the books (or watched the movies) will greatly facilitate understanding the play. Examples:

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  RON: Are you aware of the Weasleys’ Wizard Wheezes–certified nose-stealing breath?

  
  
  

  
  

  Someone who does not know what Weasley's Wizard Wheezes are will be lost here.

  
  


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  Knowing the identity of Severus Snape is necessary to follow this scene. Also, someone who has not read Book 7 might be very confused.

  
  

  
  

  HARRY: Albus Severus, you were named after two headmasters of Hogwarts. One of them was a Slytherin and he was probably the bravest man I ever knew.

  
  

  
  


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  The play mentions Cedric Diggory:

  
  

  
  

  AMOS: My son, Cedric, you do remember Cedric, don’t you?

  HARRY (remembering Cedric hurts him): Yes, I remember your son. His loss —

  AMOS: Voldemort wanted you! Not my son! You told me yourself, the words he said were, “Kill the spare.” The spare. My son, my beautiful son, was a spare.

  
  

  
  

  Without knowing much about Cedric's life and death, this scene could be quite confusing on first viewing.

  
  

These are just a few examples. Knowledge of the basic events of the entire series is necessary to completely understand the play.

That said, someone who has only seen the movies should be fine. All the important plot points are ones that were mentioned or depicted in the films, as well as the books.