The Trojan War:   A succinct (one- page) description of the history of the Trojan War can be found at: Stanford  University.
 
The war is only loosely dated as ending perhaps in 1180 b.c.e.  The Illiad was written in 700 b.c.e.


From the Perseus website (Harry Thurston Peck, Harpers Dictionary of Classical Antiquities (1898):

The main portion of the story[of the Trojan War] is contained in the two epic poems ascribed to Homer, the Iliad and the Odyssey. The incidents...were elaborated or developed by the post-Homeric poets....  While in Homer it is simply the rape of Helen which is the occasion of the war, a later legend traced its origin to the marriage of Peleus and Thetis, when Eris threw down among the assembled gods the golden apple inscribed “For the fairest” (têi kalêi). The quarrel that ensued between Heré, Athené, and Aphrodité for the prize of beauty was decided by Paris in favour of Aphrodité, who in return secured him the possession of Helen, while Heré and Athené became, from that time onward, the implacable enemies of the whole Trojan race.  [see, The Golden Apple (Apple of Discord) or see Paris in the Encyclopedia Mythica.]

According to Homer, after Helen had been carried off by Paris, Menelaüs and Agamemnon visited all the Greek chieftains in turn, and prevailed on them to take part in the expedition which they were preparing to avenge the wrong. According to the later account, the majority of the chieftains were already bound to follow the expedition by an oath, which they had sworn to Tyndareos. Agamemnon was the chosen commander-in-chief; next to him the most prominent Greek heroes are his brother Menelaüs, Achilles, and Patroclus, the two Aiaxes, Teucer, Nestor and his son Antilochus, Odysseus, Diomedes, Idomeneus, and Philoctetes, who, however, at the very outset of the expedition, had to be left behind, and does not appear on the scene of action until just before the fall of Troy. Later epics add the name of Palamedes.

The entire host of 100,000 men and 1186 ships assembled in the harbour of Aulis.

[end quote]

See also a recent article on the archeological evidence for Troy and a Trojan War (from the journal Archaeology).

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Agamemnon: is the head of the House of Atreus during the play cycle.  He was in the Trojan War (see The Iliad) because he pledges to help Menalaus, his brother, bring Helen back from Troy.
Book 11, The Iliad (Penguin, Robert Fagles, translator; excerpted from lines 17-52):

Now, suddenly, battle thrilled them more than the journey home, then sailing hollow ships to their dear native land. Agamemnon cried out too, calling men to arms and harnessed up in gleaming bronze himself. First he wrapped his legs with well-made greaves, fastened behind the heels with silver ankle-clasps, and next he strapped the breastplate round his chest... Magnificent! Ten bands of blue enamel spanned it... Then over his shoulder Agamemnon slung his sword, golden studs at the hilt, the blade burnished bright and the scabbard sheathed in silver swung on golden straps, and he grasped a well-wrought shield to encase his body, forged for rushing forays--beautiful, blazoned work. Circling the center, ten strong rings of bronze ...and there like a crown the Gorgon's grim mask-- the burning eyes, the stark, transfixing horror... And last he picked up two tough spears, tipped in bronze, honed sharp, and the glare flashed off their brazen points and pierced the high skies--and awestruck at the sight Athena and Hera loosed a crack of thunder, exalting the great king of Mycenae rich in gold.

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 House of Atreus:   The House of Atreus is marked by canabalism (Tantalus serves Pelops to the Gods as a "test" and Atreus serves all of Thyestes' children but one to him, as 'revenge') and child-death (Iphigenia sacrificed to Artemis by Agamemnon, with the hopes that the fleet can sail safely to Troy).  It is marked also by infidelity and betrayal (Clytemnestra with Aegisthus, Helen with Paris, Agamemnon with Cassandra) and matricide (Orestes kills Clytemnestra, with Electra's help).