The great screen writers and directors of the last century have nothing on Euripides when it comes to being an innovator of art. Euripides tore away the shackles of the "how to write a play" of his day--Aristotelian dramatic theory. In the process, modern Western drama was born. His play Medea is a prime example.
At first glance Medea does, in some respects, exemplify Aristotle's requirements for a tragedy. However, the play violates Aristotle's vision more than it corresponds to it. It does this through untraditional content and innovation.
In layout and movement of the plot, Medea closely matches the form of Aristotle's standard example of a tragedy--Sophocles's Oedipus Rex. Medea shares Oedipus's convention of beginning with the perspective of a mournful look back on the events that are about to be told.
Medea is highborn and descends from the lineage of the Gods. This in some ways fulfills Aristotle's requirement that the protagonist be exceptional. Likewise, both Medea and Oedipus depict what Aristotle would call "terrible and piteous events." However, this is where the similarity with Aristotle's ideal of the tragic ends.
The character of Medea is the main wrench that Euripides throws into Aristotle's description of tragedy. Aristotle's idea of the tragic hero demanded a change of experience and fortune that entails unmerited suffering on the part of the character and a fearful viewing of events on behalf of the audience. These things do not happen in Medea.
Medea has a history. She has killed spitefully and coldly in the past. She continues to do so throughout the play. She never even faces the threat of a fall from a high station because she secures sanctuary in Athens before she sets her revenge into motion (incidentally, one comes to feel like the psalmist who wrote: "I have seen a wicked and ruthless man flourishing like a green tree in its native soil"--though in this case it is a wicked woman). Euripides uses Medea to make a commentary, not to bring about that lynch-pin of Aristotelian drama: catharsis.
Medea does not attempt to meet up with Aristotle's requirements. Instead, it is becomes new form of art--tragedy as social commentary. Euripides shows himself to be among the great artistic innovators in history by his transformation of a received dramatic form into something different but wholly effective in its own way.