The main individuals involved
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 was the daughter of Leda and Zeus, sister of Clytemnestra, Castor and Pollux (the Dioscuri), and wife of Menelaus.
How the Odyssey relates?
The poem mainly focuses on the Greek hero Odysseus, king of Ithaca, and his journey home after the fall of Troy. It takes Odysseus ten years to reach Ithaca after the ten-year Trojan War. Therefor the Odyssey can be attributed to the battle of the Trojan War and his journey back home after the ten year war- Trojan war.
Homer is a mystery. The Greek epic poet credited with the enduring epic tales of The Iliad and The Odyssey is an enigma insofar as actual facts of his life go. Although very little is known about the life of Greek poet Homer, credited with being the first to write down the epic stories of The Iliad and The Odyssey.