Why does Egeus bring Hermia, Lysander, and Demetrius to Theseus?
Egeus brings Lysander, Demetrius, and Hermia to Theseus in Act I, Scene 1 to "beg the ancient privilege of Athens". Eqeus wants Hermia to marry Demetrius and she has refused because she is in love with Lysander and Lysander is in love with her.
Egeus is asking Theseus to apply the Athenian law which would send Hermia to her death for not abiding by her father's wishes.
Egeus: "As she is mine I may dispose of her:/ Which shall be either to this gentleman/ Or to her death; according to our law/ Immediately provided in that case".
Theseus choses to allow Hermia to choose her fate; she can die, marry Demetrius, or become a nun. She responds that she would rather become a nun than marry Demetrius. Theseus asks her to think on her decision, and asks her to give him her decision on his wedding day - three days away.