Agamemnon was the leader of the Greek forces in the Trojan War. He was the brother-in-law of Helen of Troy. Agamemnon was married to Clytemnestra, the sister of Menelaus' wife, Helen of Troy.
Ajax was one of the suitors of Helen and so was one of the members of the Greek force against Troy in the Trojan War. He was almost as skilled a fighter as Achilles. Ajax killed himself.
Andromache was the loving wife of the Trojan prince Hector and mother of their son, Astyanax. Hector and Astyanax were killed, Troy destroyed, and (at the end of the Trojan War) Andromache was taken as a war bride, by Neoptolemus, son of Achilles, to whom she bore Amphialus, Molossus, Pielus, and Pergamus.
Cassandra, a princess of Troy, was awarded as a war bride to Agamemnon at the end of the Trojan War. Cassandra prophesied their murder, but as was true with all her prophecies because of a curse from Apollo, Cassandra was not believed.
Clytemnestra was the wife of Agamemnon. She ruled in his stead while Agamemnon went off to fight the Trojan War. When he returned, after having murdered their daughter Iphigenia, she killed him. Their son, Orestes, in turn, killed her. Not all version of the story has Clytemnestra slaying her husband. Sometimes it is her lover.
Hector was a Trojan prince and the leading hero of the Trojans in the Trojan War.
Hecuba or Hecabe was the wife of Priam, King of Troy. Hecuba was the mother of Paris, Hector, Cassandra, and many others. She was given to Odysseus after the war.
Helen of Troy:
Helen was the daughter of Leda and Zeus, sister of Clytemnestra, Castor and Pollux (the Dioscuri), and wife of Menelaus. Helen's beauty was so overwhelming that Theseus and Paris abducted her and the Trojan War was fought to bring her back home.
Characters in the Iliad:
In addition to the list of major characters in the Trojan War above and below, for each book of the Trojan War story The Iliad, I have included a page describing its main characters.
AchillesAchilles was the leading hero of the Greeks in the Trojan War. Homer focuses on Achilles and the wrath of Achilles in the Iliad.
Iphigenia was a daughter of Clytemnestra and Agamemnon. Agamemnon sacrificed Iphigenia to Artemis at Aulis in order to obtain favorable wind for the sails of the ships waiting to sail to Troy.
MenelausMenelaus was the king of Sparta. Helen, the wife of Menelaus was stolen by a prince of Troy while a guest in the palace of Menelaus.
Crafty Odysseus and his ten-year return to Ithaca from the war at Troy.