Begin by reading about the quest for the Golden Fleece in Hamilton. Know what a harpy and an Amazon are. Know the term Argonaut (sailor on the Argo) and where the Hellespont is. Castor and Pollux were twin brothers, according to some accounts (although Hamilton gives you a different version of their lineage); they are the constellation Gemini (twins). The family is an interesting one; read about Leda and a certain swan in Hamilton. Know who Hercules and Orpheus were. The story of Medea's falling in love with Jason is echoed by Virgil in his story of Dido and Aeneas. Bear it in mind.
Euripides: To reduce the role of the gods to that of "psychological allegory" (to say, for instance, that Athena is only a way of representing Odysseus' common sense or Ares is only the urge to punch your enemy) is to shrink the scope and the intentions of the Greek writers considerably. Coleridge wrote that we ought to approach literature with a "willing suspension of disbelief." We should be able to imagine--even to believe--things we would discount in ordinary life. Otherwise, we read literature the way we read the newspaper (and many of us don't even believe what we read there). Medea doesn't simply fall in love with Jason. She is the victim of a plot devised by the gods, or rather by Hera, with the complicity of Aphrodite and Cupid, her son.
Have you noticed that there are no scene divisions in Greek plays? Have you yet made the connection between the Greek Chorus (which originally sang and danced its part) with the modern word? (How is the chorus of a modern song a bit like the speeches of the Greek chorus?)
The Nurse calls Medea a "strange woman." She is anything but typical. Euripides admits from the outset that this is a bizarre tale of an exceptional human being.
Draught-players: checkers! Suspense is not important in Greek literature. The Greeks knew all the stories and seemed to like it that way. The question is not what or whether something will happen, but how the plot will unfold. Note that we get plenty of notice that Medea is capable of anything, particularly violence against those close to her. Euripides' task, therefore, is to make Medea sympathetic--a tall order, given what we know of her.
Pain is often the source of anger and then violence. That progression is one of Euripides' main themes. "Great people's tempers are terrible." The greatness of the temper is one measure of the greatness of the person who is angry. Medea is torn by two great pains: the betrayal of Jason and her betrayal of her country and family (and consequent exile). The two are interwoven and double her sorrow. Guilt, loneliness, rejection, love, all war within her. Notice the great sorrow and sympathy of the women of Corinth (the chorus) for her. Her long absence from the stage (seven pages) serves to heighten our sympathies as well as our desire to see her--and to give Euripides a chance to fill in her history.
Medea is acutely aware of being a "foreigner" (where is she from?), and the Corinthians seem to echo that awareness, even when they are sympathizing with her. What do you think of her description of the lot of women (even strong women like herself)? Rather different from the roles of women we've seen up to now, eh (except for poor Cassandra)?
What does Creon hold against Medea? Would you take it as a curse or a compliment? (This Creon should not, of course, be confused with the Creon of Sophocles.)
Hecate = Proserpine = Artemis/Diana. Sister of Phoebus [the Sun] Apollo, she was called Phoebe, Selene, or Luna [the moon] in heaven, Diana on Earth, and Hecate or Proserpine in hell, and her power extended over all three realms. Much Shakespearian and modern witch imagery and terminology derives from the story of Medea. Some accounts make Medea the niece of Circe, the witch from the Odyssey and the granddaughter of the sun (Sol/Helius).
This is a heavily gendered play.
What of Jason? Is this the hero of the Argo and the Golden Fleece? Note in Medea's accusation (p. 16) that children make a great difference. She then brings out the full, desperate ironies of her situation. Without money or connections, she cannot wander around Greece the way a woman might bum around the United States. She would be raped, killed, or sold as a slave faster than you can say "Castor and Pollux."
Note Jason's extreme xenophobia [a good Greek word] and chauvinism [a French word] and that the fact that Medea cannot return to her homeland is her problem.
Here's Phoebus Apollo again. Everyone has some contact with Delphi sooner or later in Greek literature. What do you make of the friendship of Aegeus and Medea? Aegeus cannot promise to take Medea with him because he does not want to allow the possible charge that he has meddled in Corinth's internal affairs in some way (Creon is powerful). Note the care with which the oath is phrased.
Consider carefully the reasons why Medea wants to kill her children. Notice the references to the sun beginning on p. 40. Medea's chariot is a gift from Helius. Is she a monster?