the one-eyed giant son of Poseidon and Thoosa in Greek mythology, one of the Cyclopes described in Homer's Odyssey. His name means "abounding in songs and legends". Polyphemus first appears as a savage man-eating giant in the ninth book of the Odyssey. Some later Classical writers link his name with the nymph Galatea and present him in a different light.
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in Homeric legend a son of Neptune, the most celebrated of the Cyclops, a huge monster with one eye, who dwelt in Sicily in a cave near Ætna, and whose eye, after making him drunk, Ulysses burnt out, lest he should circumvent him and devour him, as he had done some of his companions.
And Jove said, "My child, what are you talking about? How can I forget Ulysses than whom there is no more capable man on earth, nor more liberal in his offerings to the immortal gods that live in heaven? Bear in mind, however, that Neptune is still furious with Ulysses for having blinded an eye of Polyphemus king of the Cyclopes.
Homer. The Odyssey (Butler translation)
Polyphemus is mentioned 8 times in The Odyssey
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This chain suggested, not the beams, which it was its office to transport, but the mastodons and mammoths which it might have served to harness; it had the air of the galleys, but of cyclopean and superhuman galleys, and it seemed to have been detached from some monster. Homer would have bound Polyphemus with it, and Shakespeare, Caliban.