What does Aegeus offer Medea?

Aegeus offers Medea refuge and protection in Athens after she flees from Corinth. He promises her a safe place to stay and the opportunity to start anew, provided she can help him with his own desire for children. This alliance is significant for Medea, as it gives her a chance to escape her dire circumstances and plan her next steps. Aegeus's offer highlights themes of loyalty and the potential for new beginnings amidst her tragic circumstances.