The play opens on board a ship that is being battered by a storm - or tempest. The ship's crew are hard at work trying to stop the ship from sinking.
Some passengers go up on deck.
Alonso, the King of Naples
Sebastian, Alonso's brother
Antonio, brother of Prospero (a magician, who appears later)
Ferdinand, Alonso's son
Gonzalo, a servant of Alonso
They think they are going to drown.
The action moves to an island near where the ship is in trouble. Prospero, a magician, and his daughter Miranda, are living on the island with two others.
One is Ariel (a sprite, or elf-like character) - who'd once been kept in a tree by an evil witch, Sycorax. Prospero had released him from the tree with his magic.
The other is Caliban (big and nasty, the son of Sycorax) - who Prospero had been kind to. Both Ariel and Caliban are Prospero's servants.
Prospero, we now learn, had caused the storm on purpose. It was because of something that had happened long ago, as he tells Miranda ...
Twelve years earlier, he says, Prospero was the much loved Duke of Milan, a great city in Italy. Miranda was a young princess.
Prospero was always reading. This meant that his brother Antonio (who is on the ship in the storm) had so much power that he wanted more, and plotted against Prospero, with the help of the King, Alonso.
One night, Prospero tells Miranda, he and Miranda were seized, and sent out to sea alone in an open boat. They were lucky to survive, although Prospero's magic books were on the boat. Finally they came ashore on the island where they now live.
When his story is over, Prospero makes Miranda sleep before calling for Ariel, to find out how the plans he has made for the ship in the storm are going.