Andromeda had the misfortune to be the daughter of the vain Cassiopeia, wife of King Cepheus of Ethiopia. As a result of Cassiopeia's boast that she was as beautiful as the Nereids (sea nymphs), Poseidon (sea god) sent a great sea monster to ravage the coastline.
An oracle told the king that the only way to get rid of the sea monster was to give his virgin daughter Andromeda to the sea monster; so he did, much as happened in the Roman story of Cupid and Psyche. King Cepheus chained Andromeda to a rock where the hero Perseus, still wearing the winged sandals of Hermes that he had on him from the task of decapitating Medusa, saw her. Perseus asked what had happened to her and when he heard, offered to rescue her by killing the sea monster, but on condition that her parents give her to him in marriage.
All was agreed, and Perseus slew the monster. Afterwards, during wedding preparation, Andromeda's fiance from before her enchaining, Phineus, showed up demanding his bride. Perseus argued that the surrender to her death had invalidated the contract and, failing to persuade, used the head of Medusa to turn his rival to stone.
Perseus would go on to found Mycenae where Andromeda would be queen, but first, she gave birth to their first son Perses, who stayed behind to rule when his grandfather died. (Perses was the father of the Persians.)
Their children were sons, Perses, Alcaeus, Sthenelus, Heleus, Mestor, Electryon, and a daughter, Gorgophone.
After her death, Andromeda was placed among the stars as the Andromeda constellation. The monster who was sent to ravage Ethiopia was also turned into a constellation, Cetus.
