|Medea escaping Corinth in her dragon chariot|
This one is a real tragedy, with nothing but blood and horror. Medea is a foreign princess from Colchis and a great sorceress besides; she is not Greek and seems therefore to be prone to violence. Medea and Circe both must have carried many ancient nightmares about powerful and alien women, and black magic, and so on. Medea is like a Greek man's worst nightmare: cunning, powerful, and vengeful, a womanly character gone horribly wrong. (Alcestis, the ideal Greek woman, is her opposite number.)
The original audience would have known all of the backstory well: Jason arrived in Colchis on his ship the Argo, and Medea helped him get the Golden Fleece. In order to escape with Jason, she killed her own brother and scattered pieces of him around the harbor to delay pursuit (as everyone had to collect the pieces for a proper burial before chasing Jason). They went to Iolchus, where Jason's uncle Pelias cheated him out of the throne. Medea "helped" by persuading Pelias' daughters to chop him up in hopes of performing a magic spell that would restore him to youth--which resulted in exile for Jason instead of kingship. Now they've landed in Corinth, where the play begins.
Jason has the not-so-bright idea to put Medea away and marry the princess of Corinth instead. He tries to persuade Medea that this is a great plan that will make them all financially secure, but Medea isn't buying it. As you might expect from a clever and violent sorceress, she flies into a rage and enacts a horrific revenge; she gives the princess a poisoned gown that kills both her and the king, and then murders her own beloved children in order to cause Jason maximum pain before escaping.
I said that Jason had this idea that wasn't too bright, but on the other hand, he's got quite a problem. He married a beautiful princess who helped him achieve his quest, and she turned out to be completely terrifying. You never know who she'll dismember next. It's no wonder he was hoping to get away from her (I wouldn't want to be close friends with her!), but really he is not an intelligent guy and is certainly no match for Medea.
Medea really does love her husband and her children; she wants the same things any Greek woman would want. She just has a really original method of achieving her goals...maybe that's what makes her so scary.