There were two women named Antigone ("like her ancestors") in Greek mythology.
Daughter of Oedipus
But my nature is to love... Sophocles Antigone
Antigone and Creon, International Year of the Women, 1975
Best known was Antigone ( Αντιγόνη ) the daughter of Oedipus. When Oedipus stepped down as King of Thebes, he gave the kingdom to his two sons, Eteocles and Polynices, who both agreed to alternate the throne every year. However, they showed no concern for their father, who cursed them for their negligence. After the first year, Eteocles refused to step down and Polynices attacked Thebes with his supporters (the Seven Against Thebes). Both brothers died in the battle. King Creon, who ascended to the throne of Thebes, decreed that Polynices was not to be buried, "who came back from exile, and sought to consume utterly with fire the city of his fathers," is not to be buried: "touching this man, it hath been proclaimed to our people that none shall grace him with sepulture or lament, but leave him unburied, a corpse for birds and dogs to eat, a ghastly sight of shame."
Antigone, his sister, defied the order, (explaining that "I owe a longer allegiance to the dead than to the living: in that world I shall abide for ever") but was caught. Creon decreed that she was to be locked in a cave to die, this in spite of her betrothal to King Creon's son Haemon. Antigone's sister, Ismene, then declared she had aided Antigone and wanted the same fate, although she was innocent. The gods, through the blind prophet Tiresias, expressed their disapproval of Creon's decision, which convinced him to rescind his order. He then went to bury Polynices himself. However, Antigone had already hanged herself rather than be buried alive. When Creon arrived at the tomb where she was to be interred, his son Haemon unsuccessfully attempted to murder him and then killed himself. When Creon's wife, Eurydice, was informed of Haemon's death, she, too, took her own life.
The story of Antigone has been a popular subject for books, plays and other works, including:
Antigone, one of the three Theban plays by Sophocles
Daughter of Eurytion
A different Antigone was the daughter of Eurytion and wife of Peleus.
Peleus and Telamon, his brother, killed their half-brother Phocus and fled Aegina to escape punishment. In Phthia, Peleus was purified by Eurytion and married Antigone, Eurytion's daughter. Peleus accidentally killed Eurytion during the hunt for the Calydonian Boar and fled Phthia.
Peleus was purifed of the murder of Eurytion in Iolcus by Acastus. Also in Iolcus, Peleus lost a wrestling match in the funeral games of Pelias, Acastus' father, to Atalanta. Astydameia, Acastus' wife, fell in love with Peleus but he scorned her. Bitter, she sent a messenger to Antigone to tell her that Peleus was to marry Acastus' daughter; Antigone hanged herself.
Astydameia then told Acastus that Peleus had tried to rape her. Acastus took Peleus on a hunting trip and hid his sword, then abandoned him right before a group of centaurs attacked. Chiron, the wise centaur, returned Peleus' sword and Peleus managed to escape. He pillaged Iolcus and dismembered Astydameia, then marched his army between the pieces.
Asteroid 129 Antigone
Bertolt Brecht , Antigone , Applause Books (May 1, 2000) , ISBN: 0936839252
George Steiner, Antigones : How the Antigone Legend Has Endured in Western Literature, Art, and Thought , Yale University Press (October 30, 1996) , ISBN: 0300069154
Antigone (Broadway Theatre Archive) (1974) DVD - Region 1 (U.S. and Canada only) with Geneviève Bujold, Peter Brandon Director: Gerald Freedman