Act I The one-eyed Cyclops Polyphemus, son of Neptune, god of the sea, rules over Sicily. He lives with his flock of sheep in a cave near Mount Etna. He is passionately in love with Galatea, a Nereid. But Galatea does not like the rough and brutish Polyphemus and turns him politely, but firmly, away. She is in love with the young shepherd Acis who, for his part, tenderly worships her. Odysseus and his companions land on the beach at Sicily to take a brief rest on their way home from the Trojan War. Although they have been warned about Polyphemus by Acis, the sorceress Calypso, who is disguised as a fishing woman, and her companion Nerea, the Greeks decide to stay. Calypso immediately falls in love with Odysseus. Polyphemus discovers the new arrivals and offers them his hospitality. In reality, he just wants to delay the pleasure of killing the strangers a little so he can savour it all the more. Odysseus sees through the Cyclops’s ruse but pretends to go along with it in order to devise a plan that would render the monster harmless to the advantage of all.

Act II Polyphemus learns that Galatea loves Acis and swears revenge. In the meantime, Calypso meets Odysseus. His companions are now being held captive by Polyphemus in his cave. Odysseus does not want to escape alone and abandon his companions, so he offers Polyphemus money as a ransom. Calypso reveals her true identity as a goddess and sorceress to Odysseus and offers him her help. In return, he should go with her later on to her island, Ogygia. Odysseus agrees. In the meantime, Acis and Galatea arrange to meet in a cave.

Act III Polyphemus surprises Galatea and Acis as they lie resting in a tender embrace in front of the cave. Gripped by a jealous rage, the Cyclops throws a rock at them. Acis cannot move out of the way quickly enough and is crushed. Galatea finds Acis’s dead body and wishes she was dead too. But as a goddess she is immortal. Calypso has magically transported herself and Odysseus to his companions in Polyphemus’s barricaded cave. When Polyphemus returns, Odysseus introduces himself to the giant as “Nobody” and offers him wine. Polyphemus becomes intoxicated and falls asleep. With a big burning branch, Odysseus, with the help of his companions, burns out Polyphemus’s single eye. In his agony, the Cyclops is initially helpless. The Greeks have the idea of letting themselves be carried out of the cave by the sheep, clinging onto their undersides so that Polyphemus, when he feels the sheep from above, will not touch the men and therefore not find them. The plan succeeds. Galatea hears about the way Polyphemus has been punished, and despite her satisfaction she still mourns the death of Acis. She begs Zeus to give Acis back to her and to make him immortal too. Zeus grants her wish: He brings Acis back to life and makes him god of a spring that starts to flow from the rock that Polyphemus hurled at the two lovers. Polyphemus, on the other hand, stumbles blindly around the island. He learns that he was tricked by Odysseus. Acis, now transformed into a god, curses him as a monster whose only future lies in the deepest depths of Orcus. The Cyclops feels he has been unfairly treated and calls on his father, Neptune, to take revenge on Odysseus on his behalf.