Antigone, by Sophocles, is one of three plays in the Oedipus Trilogy. Chronologically, the story of Antigone takes place after Oedipus' banishment from Thebes. While Oedipus is wandering in the wilderness looking for a place to die, his daughter Ismene finds him with the news that his sons (her brothers) Polynices and Eteocles have quarreled over who is to rule Thebes. Polynices has left home to find help and support for his claim to the throne. He eventually comes to Oedipus for support, and in one final moment of impatient rage, Oedipus curses his two sons, announcing that they will kill one another.
This is exactly what happens. Eteocles and Creon (Oedipus' brother in law) defend Thebes against Polynices and Adrastus (king of a neighboring city). The brothers eventually kill one another in battle.
As a result, Creon is made king. He issues a decree that Eteocles shall have a hero's funeral with full burial rites, because he died fighting for Thebes. Polynices' body, he declares, is not to be touched, because he was a traitor. Meanwhile, Ismene and Antigone (sisters and Oedipus' only remaining children) are left helpless to bury their brother Polynices, whose soul they believe will never enter the afterlife if his body is not properly buried (it was the women's job in this culture to take care of the dead).
Antigone, more courageous than her sister, defies Creon's decree and buries her brother. Creon, without knowing who did it, announces that the person guilty of the act will be punished by death. The rest of the drama basically shows how Antigone stands up for what she believes in, even though it means fighting her own family and risking her life.