From just reading Agamemnon on its own, you might not immediately think that "Justice and Judgment" is its most important theme. Like, sure, it would be in your Top 10, but it probably wouldn't be top dog. Instead, you might want to put "Revenge" first, or maybe "Fate and Free Will." And that would be cool. So why are we putting it first? That's because "Justice and Judgment" is definitely the main theme of the Oresteia trilogy as a whole; as you may remember, Agamemnon is only the first part of this trilogy.
Appropriately enough, given that it's only part 1 of 3, the picture of justice that emerges from Agamemnon is pretty confused. Most characters in the play view it as a form of payback: you hurt me, so I hurt you. This gets complicated, however, like when Aegisthus considers it an act of justice to kill Agamemnon, even though Agamemnon never did anything directly to him. Instead, Aegisthus's variation on the payback theme would go something like this: your dad hurt my siblings and my dad, so I hurt you.
If this sounds more like revenge to you than justice, you're definitely on to something – but we'll talk about that more under the "Revenge" theme. For now, we'll simply point out one more problem about justice in Agamemnon: the idea that justice comes from Zeus, the king of the gods. This idea mainly comes from the Chorus, and it kind of makes sense, since Zeus likes to protect the laws of hospitality and nice stuff like that. The idea breaks down, however, when the Chorus claims (in line 1486) that Zeus is "all-causing" and "all-doing." If this is true, and Zeus is responsible for literally everything that happens, doesn't that mean he's responsible for injustice as well as justice? Or is injustice itself really justice, because it's all part of Zeus's plan? It would be pretty hard to argue that some of the things mentioned in the play – like the crime of Atreus – are really, deep down, in accordance with justice. So, basically, what we're getting at is that the treatment of justice in this play is a major mind-bender, and we can definitely tell why Aeschylus had to write two more plays just to get the issue under some sort of control.
According to the characters in Agamemnon, there is no difference between revenge and justice.
The death of Cassandra is both sanctioned by the gods and also unjust.