Final answer:
Odysseus's relationship with Calypso is one of captor and captive, with Calypso desiring to keep him on her island while he yearns for home. Despite her offers of immortality and love, Odysseus remains focused on returning to Ithaca, and eventually, the gods command Calypso to let him go.
Step-by-step explanation:
Odysseus's relationship with Calypso in Homer's epic The Odyssey is complex and multifaceted. Calypso is a nymph who rescues Odysseus when he is adrift at sea and brings him to her island, Ogygia. There, she provides him comfort and promises immortality if he remains with her, effectively making him her lover and captive for several years. However, Odysseus longs to return to his wife and home in Ithaca. Despite the hospitality and affection Calypso shows towards Odysseus, he does not reciprocate her desire to keep him there forever. The gods intervene, and at the command of Zeus, Calypso reluctantly allows Odysseus to leave the island and resume his journey home.