There are a lot of stories that can go in here: the various adventures of the dioscuri, Theseus abducting Helen and the oath of the horse.... But those are all other Mondays. For now, it will suffice you to know that Helen was married off to Menelaus of Sparta, and Clytemnestra was married to Agamemnon of Mycenae, the sons of Atreus.
So Paris takes Helen off to Troy and the Trojan War starts (that's next Monday). Agamemnon is the leader of all of the Greeks. They're getting ready to leave for Troy (launching a thousand ships) but they can't get a good wind. So Agamemnon gets an oracle that he needs to appease Artemis, and that to do this he has to sacrifice his daughter Iphegenia. So he does this, and off they sail to Troy. They wage war for ten years, until they eventually win and return home.
Clytemnestra, Agamemnon's wife, is understandably angry that he's killed her daughter. While he's away, she takes Aegisthus, Agamemnon's cousin and Thyestes' son, as her lover. They plan to kill Agamemnon in revenge when he returns.
Agamemnon returns to Mycenae with Cassandra, the princess of Troy with a gift for prophecy.
Cassandra:
Apollo, Apollo!
Lord of the ways, my ruin.
Where have you led me now at last? What house is this?
Chorus:
The house of the Atreidae. If you understand
not that, I can tell you; and so much at least is true.
Cassandra:
No, but a house that God hates, guilty within
of kindred blood shed, torture of its own,
the shambles for men's butchery, the dripping floor.
Apollo, Apollo!
Lord of the ways, my ruin.
Where have you led me now at last? What house is this?
Chorus:
The house of the Atreidae. If you understand
not that, I can tell you; and so much at least is true.
Cassandra:
No, but a house that God hates, guilty within
of kindred blood shed, torture of its own,
the shambles for men's butchery, the dripping floor.
In the Greek world, a son is bound by honour to revenge his father's murder. Orestes, Agamemnon's son, is therefore bound to kill Clytemnestra. But there's a problem. Seeing as Clytemnestra is his mother, he'll be cursed if he kills her, and Aegisthus too. Anyway, eventually Orestes does kill his mother, in The Libation Bearers. And then throughout The Eumenides, he's chased by the furies and cursed for his mother's death. Eventually, he makes penance for his actions, and finally, Orestes is the one who breaks curse of the Tantalids.