This story is written by Theocritus.
Like many of the monstrous creatures of the earth, the Cyclops Polyphemus were banned from the earth by Zeus, but they were re-admitted back and became a favorite of Zeus, for they were great workmen. Zeus had given them a home in a country where the vineyards and cornlands bore fruits in plentiful numbers, even though no seeds had been planted. The Cyclops Polyphemus lived well off of the sheep and goats that lived in the country. The fierceness of the Cylcops Polyphemus grew as time passed. There wasn't any justice in the country and it soon became a bad place for strangers to visit.
Many years after the Prometheus had been punished, and the descendants of the men he helped had become civilized and had learned how to build ships, a Greek prince by the name of Odysseus (Ulysses in Latin) beached his boat on the shore of the land where the Cyclops Polyphemus lived. He was returning home after the destruction of Troy. He and twelve men began to explore the land. They encountered a cave which appeared to be inhabited that was surrounded by a fence; this fence was open. They made their way through the fence towards the cave, holding a pouch full of wine to give to any inhabitants, in return for the hospitality that they would provide them with. They proceeded into the cave, realizing soon that it was home to a very prosperous man. Lining the walls were many items including food and skins of lamb. The twelve men feasted on the food in the cave, waiting for the owner of the dwelling to arrive.
A large, hideous man finally arrived into the cave, and closed the opening of the cave with a large stone. He caught sight of the strangers and asked who they were. Odysseus replied by saying that they were warriors from Troy under the protection of the god, Zeus. Polyphemus, the great beast, replied by saying that he didn't care for Zeus. With that, he picked up two of the men, and devoured the men. He became tired soon and slept. This put Odysseus into a predicament; he could wait for Polyphemus to wake up and move the stone, or they could kill the beast, but since Polyphemus was the only one who could move the stone, but they would be imprisoned forever.
During that night, Odysseus tried desperately to think of a plant to escape from the cave. However, when day broke and Polyphemus had woken to the sound of the sheep outside the cave, he had not thought of an idea. He watched as Polyphemus devoured two more of his men. Polyphemus removed the flock from around the cave, easily opening and closing the cave stone as if it were a feather. Odysseus still remained in the cave throughout the day. While Polyphemus was away, Odysseus had thought up a plan that could save him from being eaten by the dreadful beast. An enormous timber lay near the pens of the flocks and it was as long and as thick as a twenty-oared ship. They cut off a piece of the timber and sharpened and hardened it to a point. By the time the Cyclops had returned, they had already finished it and hid it in the cave. Two more men were consumed by the Cyclops. Odysseus offered some wine to Polyphemus. He eagerly drank it and demanded more. The Cyclops had drunk so much that it fell into a drunken sleep. Odysseus and his men quickly found the stake and heated the point of the stake until it almost burst into flames. Quickly, they drove the red-hot spike of the stake right into the one eye of the Cyclops. Now blind, Polyphemus searched for the men in the cave but was unsuccessful, however the six men had slipped away. The Cyclops removed the stone away but he put his arm across the entrance, hoping to catch the men who were trying to escape. Odysseus knew that Polyphemus would do this. Each day the Cyclops would let the flock out into the pasture and this was the way that the men were going to escape. They strapped themselves to the underside of the rams. When the Cyclops felt over the rams to make sure that no men would be on their backs, he neglected to feel the underside of the rams. And this was the way that the men would escape from the cave.
When Odysseus reached a safe distance from the cave, he taunted the blind Cyclops. This brought Polyphemus' blood to a boil. He stormed from the cave in search of Odysseus and the others. He pulled a great chunk of out a mountain and hurled it at the men on their ship. It came very close to the ship, narrowly missing it. The waves from the rock that was thrown caused their boat to be pushed back towards the shore. The men desperately tried to pull the ship back out to sea and luckily succeeded. When safely back into the sea, Odysseus taunted Polyphemus again. He told the Cyclops to tell anyone who asked who the man who made him go blind.
Centuries passed before anyone heard from the Cyclops. The next story people heard about Polyphemus put him in a positive light. Like many say, evil and ugly things change and grow milder with time. The storyteller who told this story probably pitied the helpless Cyclops, now blind. The Cyclops was now madly in love with Galatea, the sea nymph. He had moved to the island of Sicily and had now mysteriously got his eye back, perhaps by a miracle from his father in this story, Poseidon. Polyphemus knew that he could never have Galatea. But whenever his pain made him harden his heart against her, the minx would come softly stealing near him. Then a shower of apples would pelt his flock and her voice would ring in his ears calling him a laggard in love. When he tried to chase her, she would be off, laughing at his slow clumsiness. All he could do was sit at the shore, like he did when Odysseus left from his cave.
In a much later story, Galatea became a kind being, not because of she fell in love with the hideous Cyclops, but because she reflected that he was the favoured son of the Lord of the Sea. So she told her sister nymph, Doris, who had rather hoped to attract the beast herself.
Polyphemus never won Galatea. She fell in love with a young prince named Acis, whom Polyphemus, furiously jealous, killed. We are not told that the Cyclops ever loved any maiden with the exception of Galatea or that any maiden ever loved the one-eyed Cyclops.