The theme of "Revenge" is also closely connected with the theme of "Justice and Judgment." Agamemnon, if you remember, is only the first part of a three-part series of tragedies entitled the Oresteia. Most scholars think that the Oresteia as a whole charts the progress of ancient Greek civilization from an earlier stage, in which people took the law into their own hands, and a later stage in which crimes were punished by courts of law. According to this model, Agamemnon represents the more primitive stage that had to be corrected by later development.
When looking at the whole trilogy, this might be a good way of thinking about it, but let's try not to get ahead of ourselves when looking at Agamemnon specifically. In reading the play, you'll notice that the word "justice" gets passed around quite a lot, sometimes in contexts very close to what we would call revenge. For example, at the end of the play, Aegisthus strikingly says that the murder of Agamemnon proves to him that the gods are just. Is there really a difference in Agamemnon between vengeance and justice? Is it possible to take justice into your own hands, or does doing so just make it revenge? What is the point of revenge, anyway?
Aeschylus's play is designed to show that revenge only leads to more violence.
Agamemnon portrays the gods as just as vengeful as human beings.