Book one is called "The Rage of Achilles" however there's a lot of angry bods at the start of The Iliad. It's like picking up a book that's number five in a series and wondering what's going on. Fortunately I know some of the cast already:
Zeus – Top god, none of the other gods really want to talk to him about the war as he's got a bit of a temper.
Apollo – God of sun, prophecy, etc, etc, angry at Agamemnon. Likes a good sing-song and is good with a bow and arrow.
Hephaestus - Disfigured husband of Aphrodite, last time Zeus got angry with him, he got thrown off a cliff.
Hera - Wife of Zeus, doesn't fancy standing up to him either.
Agamemnon – Commander of the Achaean army, has managed to piss off Apollo.
Achilles – Dangled into the river Styx as a babe and therefore invincible except for his heel. Good at running and archery. I don't think the heel myth is covered by The Iliad though.
Thetis - sea nymph and mother of Achilles.
Achaeans – they'd be what we'd call the Greeks, backed by Hera.
Trojans – the other army, defending the city of Troy (otherwise known in Latin as Ilium).
We're well into the Trojan war at this point and the Greeks aren't doing so well. The gods do like to meddle in the lives of men and with all that anger going on, Apollo has unleashed a plague against them.
I knew this before I started; there's just too many characters in The Iliad. Homer had a tendency to talk about people via who their parents were which can either work for or against you. I just find I'm not sure who's talking or being talked about already. I hope this is just because it's the start...
So there's your introduction.