Odysseus and Polyphemus

The Cicones
After Odyseus left Troy he came first to the island of the Cicones. At the island of the Cicones Odysseus and his men stormed the beach but didn't press any attack on the people there. The Cicones rallied back up and prepared for an attack on Odysseus and his men, from horse back. In a large battle that Odysseus inevitably lost, six rows of Odysseus's men were killed and Odysseus had to flee the island

The Lotus-Eaters
When Odysseus and his men landed on the island of the Lotus-Eaters, Odysseus sent out a scouting party of three or so men who ate the lotus with the natives. This caused them to fall asleep and stop caring about going home, and desire only to eat the lotus. Odysseus went after the scouting party, and dragged them back to the ship against their will. He set sail, with the drugged soldiers tied to the rudder benches to prevent them from swimming back to the island.

Polyphemus

Odysseus offering wine to the CyclopsA scouting party, led by Odysseus and his friend Misenus, landed in the territory of the Cyclops and ventured upon a large cave. They entered and proceeded to feast on the livestock that they found there. Unbeknownst to them, the cave was the dwelling of Polyphemus, a one-eyed giant who soon returned. Refusing hospitality to his uninvited guests, Polyphemus trapped them in the cave by blocking the entrance with a boulder that could not be moved by mortal men. He then proceeded to eat a pair of them everyday, but Odysseus devised a cunning plan.
To render Polyphemus unwary, Odysseus gave him a bowl of the strong, unwatered wine given them by Maron, the priest of Apollo. When Polyphemus asked for his name, Odysseus told him that it was "Nobody". (Οὔτις, "Nobody", is also a short form of his own name.) In appreciation for the wine, Polyphemus offered to return the favour by only eating him last. Once the giant fell asleep, Odysseus and his men turned an olive tree branch into a giant spear, something that they prepared while Polyphemus was out of the cave shepherding his flocks, and blinded him. Hearing Polyphemus's cries, other Cyclopes come to his cave to ask what was wrong. Polyphemus replied, "Οὖτίς με κτείνει δόλῳ οὐδὲ βίηφιν." ("Nobody is killing me either by treachery or brute violence!") The other Cyclopes let him be, thinking that his outbursts must be either madness or the will of the gods.

In the morning, Polyphemus rolled back the boulder to let the sheep out to graze. Now blind, he could not see the men, but he felt the tops of his sheep to make sure that the men were not riding them, and spread his arm at the entrance of the cave. Odysseus and his men escaped, however, by tying themselves to the undersides of three sheep each. Once out, they loaded the sheep aboard their ship and set sail.

As Odysseus and his men were sailing away, he revealed his true identity to Polyphemus. Enraged, Polyphemus tried to hit the ship with boulders, but, because he was blind, he missed, although the rocks landed very close to the ship, swaying it with billows. When the ship appeared to be getting away at last, Polyphemus raised his arms to his father, Poseidon, and asked him to not allow Odysseus to get back home to Ithaca. If he did, however, he must arrive alone, his crew dead, in a stranger's ship.

This event is the setting for the only surviving complete satyr play, Cyclops by Euripides. This version contains a more humorous version of the story by including the cowardly satyrs.

According to Virgil's Aeneid, Achaemenides was one of Odysseus' crew who stayed on Sicily with Polyphemus until Aeneas arrived and took him with him. Virgil was probably trying to interweave his tale as much as possible with Homer's already ancient, great work, especially as Achaemenides had nothing to do with the story at all and was in fact never mentioned again.

Aeolus
Continuing his journey, Odysseus stopped at Aeolia, the home of Aeolus, the favoured mortal of the gods who received the power of controlling the winds. Aeolus gave Odysseus and his crew hospitality for a month, in return for Odysseus's interesting stories. Aeolus also provided a bag filled with all winds but the one to lead him home. Because Odysseus guarded the bag for the entire voyage home, without so much as a wink of sleep, his crew suspected that some treasure might be in it. A couple of them decided to open it as soon as he fell asleep—just before their home was reached. They were immediately blown back to Aeolia by a violent storm. Aeolus refused to offer any more help because he realised Odysseus must be cursed by the gods. Odysseus had to begin his journey from Aeolia to Ithaca over again. Although heartbroken, he hid his feelings from his crew.

The Laestrygonians
They came next to Telepylos, the stronghold of Lamos, king of the Laestrygonians. Odysseus's ships entered a harbor surrounded by steep cliffs, with a single entrance between two headlands. The captains took their ships inside and made them fast close to one another, where it was dead calm. Odysseus kept his own ship outside the harbour, moored to a rock. He climbed a high rock to reconnoiter, but could see nothing but some smoke rising from the ground. He sent two of his company with an attendant to investigate the inhabitants.

The men followed a road and eventually met a young woman, who said she was a daughter of Antiphates, the king, and directed them to his house. When they arrived there, however, they found a gigantic woman, the wife of Antiphates who promptly called her husband. He immediately left the assembly of the people and, on arrival, snatched up one of the men and started to eat him. The other two ran away, but Antiphates raised a hue-and-cry. Soon they were pursued by thousands of Laestrygonians—giants, not men—who threw vast rocks from the cliffs, smashing the ships, and speared the men like fish.
Odysseus escaped with his single ship due only to the fact that it was not trapped in the harbour. The rest of his company was lost. The surviving crew traveled to the island of Circe

Circe
The next stop was Aeaea, the island of Circe, the enchantress, where Odysseus sent ahead a scouting party. Circe invited the scouting party to a feast and turned all the men into pigs with a wand after they ate food laced with one of her magical, sleep-inducing potions. Only Eurylochus, suspecting treachery from the outset, escaped to warn Odysseus and the others who had stayed behind with the ships.

Odysseus, against his fellows' bidding, set forth to rescue his transfigured men but was intercepted by Hermes and told to procure the herb moly, which would protect him from a similar fate. When it snubbed her magic, she offered to sleep with Odysseus, but, fellowing Hermes's counsel, he first demanded that she turn his crew back into humans. This she did, and Odysseus obliged, staying with her for a year. He eventually left Aeaea at the insistence of his crew, with whom Circe agreed. She gave him advice about the remainder of his journey. During the preparation for departure, however, Odysseus' youngest crewman, Elpenor fell from a roof and died.
Circe subsequently bore Odysseus a son, Telegonus, who would eventually cause his father's death

Journey to the Underworld
After speaking to Circe, Odysseus decided to talk with Tiresias, so he and his men journeyed to the River Acheron in Hades, where they performed sacrifices which allowed them to speak to the dead. Odysseus sacrificed a ram, attracting the dead spirits to the blood. He held them at bay and demanded to speak with Tiresias, who told him how to pass by Helios's cattle and the whirlpool Charybdis. Tiresias also told him that, after his return to Ithaca, he must take a well-made oar and walk inland with it to parts where no-one mixes sea salt with food, until someone asks him why he carries a winnowing fan. At that place, he must fix the oar in the ground and make a sacrifice to appease Poseidon. Tiresias also told Odysseus that, after that was done, he would die an old man, "full of years and peace of mind"; his death would come from the sea and his life ebb away gently. (Some read this as saying that his death would come away from the sea.)

While in Hades, Odysseus also met Achilles (who told him that he would rather be a slave on earth than the king of the dead), Agamemnon and his mother, Anticlea. The soul of Ajax, still sulking about Achilles's armor, refused to speak to Odysseus, despite the latter's pleas of regret.
Odysseus also met his comrade, Elpenor, who told him of the manner of his death and begged him to give him an honorable burial.

The Sirens
Circe had warned Odysseus of the dangers of the singing creatures who lured men to their death on the rocks around their island. She advised him to avoid them but said that, if he really felt that he must, he should have his men plug their ears with beeswax and tie him to the mast to keep him from escaping.

Odysseus had his men do so. As they passed the island, the three Sirens began to sing beautifully, promising him wisdom and knowledge of past and future. Enchanted by their song, he struggled and tried to break free, but two of his men bound him even more tightly until they passed beyond the island

Scylla and Charybdis
Odysseus had been told by Circe that he would have a choice between two paths home. One was the Wandering Rocks, where either all made it through or all died, and which had only been passed by Jason, with Zeus's help. Odysseus, however, chose the second path: on one side of the strait was a whirlpool called Charybdis, which would sink the ship; on the other was a monster called Scylla, daughter of Crataeis, who had six heads and could seize and eat six men.

King of Ithaca, husband of Penelope, father of Telemachus, and son of Laërtes and Anticlea, Odysseus is renowned for his guile and resourcefulness, and is hence known by the epithet Odysseus the Cunning. (See mētis, or "cunning intelligence"). He is most famous for the ten eventful years he took to return home after the Trojan War.

Polyphemus (Greek: Πολύφημος, transliterated as Polyphemos in Robert Fitzgerald's translation) is a character in Greek mythology, one of the Cyclops. The one-eyed son of Poseidon and Thoosa, his name means "famous"[1]. Polyphemus plays a pivotal role in Homer's Odyssey.