The following summary of Medea is due to SparkNotes.
Euripedes' Medea opens in a state of conflict. Jason has abandoned his wife, Medea, along with their two children. He hopes to advance his station by remarrying with Glauce, the daughter of Creon, king of Corinth, the Greek city where the play is set. All the events of play proceed out of this initial dilemma, and the involved parties become its central characters.
Outside the royal palace, a nurse laments the events that have lead to the present crisis. After a long series of trials and adventures, which ultimately forced Jason and Medea to seek exile in Corinth, the pair had settled down and established their family, achieving a degree of fame and respectability. Jason's recent abandonment of that family has crushed Medea emotionally, to the degree that she curses her own existence, as well as that of her two children.
Fearing a possible plot of revenge, Creon banishes Medea and her children from the city. After pleading for mercy, Medea is granted one day before she must leave, during which she plans to complete her quest for "justice"--at this stage in her thinking, the murder of Creon, Glauce, and Jason. Jason accuses Medea of overreacting. By voicing her grievances so publicly, she has endangered her life and that of their children. He claims that his decision to remarry was in everyone's best interest. Medea finds him spineless, and she refuses to accept his token offers of help.
Appearing by chance in Corinth, Aegeus, King of Athens, offers Medea sanctuary in his home city in exchange for her knowledge of certain drugs that can cure his sterility. Now guaranteed an eventual haven in Athens, Medea has cleared all obstacles to completing her revenge, a plan which grows to include the murder of her own children; the pain their loss will cause her does not outweigh the satisfaction she will feel in making Jason suffer.
For the balance of the play, Medea engages in a ruse; she pretends to sympathize with Jason (bringing him into her confidence) and offers his wife "gifts," a coronet and dress. Ostensibly, the gifts are meant to convince Glauce to ask her father to allow the children to stay in Corinth. The coronet and dress are actually poisoned, however, and their delivery causes Glauce's death. Seeing his daughter ravaged by the poison, Creon chooses to die by her side by dramatically embracing her and absorbing the poison himself.
A messenger recounts the gruesome details of these deaths, which Medea absorbs with cool attentiveness. Her earlier state of anxiety, which intensified as she struggled with the decision to commit infanticide, has now given way to an assured determination to fulfill her plans. Against the protests of the chorus, Medea murders her children and flees the scene in a dragon-pulled chariot provided by her grandfather, the Sun-God. Jason is left cursing his lot; his hope of advancing his station by abandoning Medea and marrying Glauce, the conflict which opened the play, has been annihilated, and everything he values has been lost through the deaths that conclude the tragedy.