I wholeheartedly agree with everything Amy has thus far said about the idea of gender roles in Medea, but there are a few other thoughts/ideas that recur throughout the play as well:
Another main thought/idea of Medea is that of the ‘torn nuclear family.’ This all begins right at the beginning of the play, in the first 16 lines, when Jason decides to abandon Medea and his first two children to remarry Glauce. Ultimately this decision comes down to a quest for power by Jason, and this becomes more evident as the play goes on. This thought is Euripides comment on how he thinks people often act in Greek society.
Another prevalent thought that goes hand-in-hand with the familial problems is that of how to handle revenge. Early on in the play, the Nurse becomes afraid of Medea and her thirst for revenge against Jason, because it is becoming all consuming. Medea even discusses wanting to go so far as to hurt her own children just so that she can get back at Jason for the pain he has caused her. Euripides wants to show the idea that someone going through intense emotional stress doesn’t just turn against the cause, but rather against the entire world around them (evidenced in lines 95-96, and 110-114). Under normal circumstances, any loving mother, no matter how angry, would never want to hurt her own children for an act of revenge.
This line of thought continues in lines 659-660 as the Chorus curses men for unlocking female desire and then “disowning” it. Which shows that a person’s anger for revenge affects even other people and has them thinking ill thoughts about others (ie: Medea desiring revenge on Jason so badly that some of that anger rubs off on the Chorus until they too begin to dislike men, more).
In lines 796-797 Euripides shows just how strong and overwhelming the desire for revenge can be to a person. Medea is quoted as saying, “Yes, I can endure guilt, however horrible; the laughter of my enemies I will not endure.” At this point, her desire for revenge on Jason is so intense that she sees nothing but her ultimate goal. Medea is so blinded by her desire for revenge that nothing else in her world takes precedence over that thought. And, it is also known that it is a conscious decision by Medea to feel this way, because she says that she “will not endure.” Had she said “can not endure,” it would mean that she had no choice, but the use of ‘will’ means that she is making the decision to deal with the guilt about killing her own children if it serves her ultimate goal.
Another place where Medea almost openly admits to giving in to her desire for revenge is in line 1076, where she says “Anger, the spring of all life’s horror, masters my resolve.” This is the point where Medea has completely given herself to her desires for revenge. In line 1053 Medea even goes so far as to call her own children a “sacrifice.”
All of these thoughts/ideas stem directly from things that Medea herself says to different other characters in the play. Euripides is not 100% clear about his personal thoughts on the desire for revenge, but I think that he feels that revenge is something that is dealt with on a day to day basis in Greek society, for a multitude of reasons, but the struggle for power would be the most prominent. The thought/idea of a burning desire for revenge takes a back seat to Euripides thoughts/ideas on feminism (Medea’s main focal point), but none-the-less is still a prominent idea within the play, and worth considering because it still has much relevance today.