In Greek mythology, Andromeda (/ænˈdrɒmɪdə/; Ancient Greek: Ἀνδρομέδα, romanized: Androméda or Ἀνδρομέδη, Andromédē) is the daughter of Cepheus, the king of Aethiopia, and his wife, Cassiopeia. When Cassiopeia boasts that she (or Andromeda) is more beautiful than the Nereids, Poseidon sends the sea monster Cetus to ravage the coast of Aethiopia as divine punishment. Queen Cassiopeia understands that chaining Andromeda to a rock as a human sacrifice is what will appease Poseidon. Perseus finds her as he is coming back from his quest to decapitate Medusa, and brings her back to Greece to marry her and let her reign as his queen. With the head of Medusa, Perseus petrifies Cetus to stop it from terrorizing the coast any longer.

As a subject, Andromeda has been popular in art since classical antiquity; rescued by a Greek hero, Andromeda's narration is considered the forerunner to the "princess and dragon" motif. From the Renaissance, interest revived in the original story, typically as derived from Ovid's Metamorphoses. The story has appeared many times in such diverse media as plays, poetry, novels, operas, classical and popular music, film, and paintings. A significant part of the northern sky contains several constellations named after the story's figures; in particular, the constellation Andromeda is named after her.

The Andromeda tradition, from classical antiquity onwards, has incorporated elements of other stories, including Saint George and the Dragon, introducing a horse for the hero, and the tale of Pegasus, Bellerophon's winged horse. Ludovico Ariosto's epic poem Orlando Furioso, which tells a similar story, has introduced further confusion. Patricia Yaker Ekall has criticized the tradition of depicting the princess of Aethiopia as white; noting few artists have chosen to portray her as dark-skinned, despite Ovid's account of her. Others have stated that Perseus's liberation of Andromeda was a popular choice of subject among male artists, reinforcing a narrative of male superiority with its powerful male hero and its endangered female in bondage.

The name is Greek (Ἀνδρομέδα, Androméda), perhaps meaning 'mindful of her husband': from the noun ἀνήρ, ἀνδρός, anḗr, andrós 'man'; and either the verb μέδεσθαι, medesthai 'to be mindful of', from μέδω, médō, 'to protect, rule over', or the verb μήδομαι, mḗdomai 'to deliberate, contrive, decide'. These verbs are related to μήδεια, mḗdeia 'plans, cunning', the likely origin of the name of Medea, the sorceress.

In Greek mythology, Andromeda is the daughter of Cepheus and Cassiopeia, king and queen of the kingdom of Aethiopia. Her mother Cassiopeia foolishly boasts that she is more beautiful than the Nereids, a display of hubris by a human that is unacceptable to the gods. To punish the queen for her arrogance, Poseidon floods the kingdom's coast and sends a sea monster named Cetus to ravage its inhabitants. In desperation, King Cepheus consults the oracle of Ammon, who announces that no respite can be found until the king sacrifices his daughter, Andromeda, to the monster. She is thus stripped naked and chained to a rock in Jaffa by the sea to await her death. Perseus is just then flying near the coast of Aethiopia on his winged sandals or on Pegasus the winged horse, having slain the Gorgon Medusa and carrying her severed head, which instantly petrifies any who look at it. Upon seeing Andromeda bound to the rock, Perseus falls in love with her, and he secures Cepheus's promise of her hand in marriage if he can save her. Perseus kills the monster with the Medusa's head, saving Andromeda. Preparations are then made for their marriage, in spite of her having been previously promised to her uncle, Phineus. At the wedding, a quarrel between the rivals ends when Perseus shows Medusa's head to Phineus and his allies, turning them to stone.

Andromeda follows her husband to his native island of Seriphos, where he rescues his mother, Danaë from her unwanted wedding to the king of that island. They next go to Argos, where Perseus is the rightful heir to the throne. However, after accidentally killing his grandfather Acrisius, the king of Argos, Perseus chooses to become king of neighboring Tiryns instead. The mythographer Apollodorus states that Perseus and Andromeda have six sons: Perses, Alcaeus, Heleus, Mestor, Sthenelus, Electryon, and a daughter, Gorgophone. Their descendants rule Mycenae from Electryon down to Eurystheus, after whom Atreus attains the kingdom. The Greek hero Heracles is also a descendant, as his mother Alcmene is the daughter of Electryon.

According to the Catasterismi, Andromeda is placed in the sky by Athena as the constellation Andromeda, in a pose with her limbs outstretched, similar to when she was chained to the rock, in commemoration of Perseus' bravery in fighting the sea monster.

The myth of Andromeda was represented in the art of ancient Greece and of Rome in media including red-figure pottery such as pelike jars, frescoes, and mosaics. Depictions range from straightforward representations of scenes from the myth, such as of Andromeda being tied up for sacrifice, to more ambiguous portrayals with different events depicted in the same painting, as at the Roman villa in Boscotrecase, where Perseus is shown twice, space standing in for time. Favoured scenes changed with time: until the 4th century BC, Perseus was shown decapitating Medusa, while after that, and in Roman portrayals, he was shown rescuing Andromeda.