The poet invokes the Muse to help him tell the story of Odysseus. How original.
We learn that Poseidon, god of the sea, holds a grudge (though we don't know exactly why) against Odysseus and is making the guy's voyage home a pretty difficult.
This tells us two very important things: (1) Greek gods are temperamental, and (2) Poseidon is a powerful guy.
So Poseidon isn't around on Mount Olympos (presumably because he's busy getting sweet revenge), while the other gods discuss the fact that this one guy Orestes murdered this other guy Aigisthos.
Zeus, king of the gods and playa-extraordinaire, says that Aigisthos totally deserved it because he had a long affair with Agamemnon's wife while he was away at Troy and then killed Agamemnon upon returning home.
Turns out Aigisthos had been warned by Hermes (the messenger of the gods) not to do this. In fact, Hermes pretty much explicitly said, "If you touch this guy's wife and then kill him, then Orestes is going to pop a cap in you." And still Aigisthos ignored the advice.
Plus, because Orestes is Agamemnon's son, he was only avenging his father by killing Aigisthos. The Greeks were pretty serious about the whole avenging-the-father thing. Let's just call it "justifiable homicide" in the eyes of the gods.
Athene, who clearly doesn't give a crab's apple about Orestes, decides Zeus should be thinking less about him and more about her all time favorite mortal, Odysseus. So she asks for Zeus (who is her father, by the way) to have mercy on her favorite captain, who's has been trying to get home now for something around ten years—in addition to the ten years he was away fighting the Trojan War.
Zeus claims that hasn't forgotten Odysseus's plight, though we all know he's just making excuses.
Zeus reveals a little more of the Poseidon grudge story: the god is angry with Odysseus because the mortal poked out the eye of Polyphemos, Poseidon's son.
Zeus comments that Poseidon will need to stop pouting at some point and get over himself already, since all the other gods like Odysseus so much.
We learn that Odysseus at this very moment is being held captive by a nymph named Kalypso.
Athene wants to send the gods' messenger Hermes to go tell Kalypso that she really needs to let Odysseus go (you know, so he can get back to his wife and child and all).
Zeus, to remind everyone that HE'S THE BOSS, decides not to send Hermes. Yet.
But Athene, reminding everyone that in fact, she's the boss, goes to Ithaka disguised as Mentes, a family friend of Odysseus's and the ruler of the Taphians. Oh, and also a man.
Which brings us to Ithaka, where a bevy of suitors is milling about (for reasons which will be soon disclosed).
Once Mentes/Athene arrives, these suitors do what they do best, namely lounge around lazily. Odysseus's son Telemachos, very clearly neither lazy nor a suitor, gets up hastily to welcome his guest. He even prepares a banquet in Mentes's honor.
Historical Context Note: Hospitality (called xenia)was a big deal in the ancient world. When guests showed up, they were expected to be good guests (bring gifts and behave themselves). Likewise, the hosts were expected to, well, be good hosts (provide food and shelter). Just keep in mind that breaking these rules was a huge social taboo. And if Miss Manners gets you excited, check out our "Hospitality" theme.
So Telemachos apologizes to Mentes for the suitors' rudeness, hints that it would be different if his father were here, and asks who this guest is.
The point is, Telemachos didn't know this guest was Mentes (or Athene), yet he still pulled out all the stops to play the good host.
Athene responds as Mentes and advises the boy to not give up hope of his father Odysseus coming home.
She asks about the suitors and Telemachos replies that he can't make them go away; he wishes Odysseus were here to fend them off.
Why? Well, we learn that the suitors are selfishly eating all of the household's food and giving nothing in return while hoping Odysseus's wife Penelope will marry one of them.
See, Odysseus has taken so long coming back from the Trojan war they're all convinced he's dead. Also, Penelope is super-attractive, plus her husband would get Ithaka.)
Anyway, trying to marry your absent host's wife is a good example of breaking the guest-host bond of good behavior.
So Athene advises Telemachos to go to Pylos and talk to Nestor, and then head to Sparta to see King Menelaos, who has red hair. Which apparently matters.
And when he's done with this, he should think about how to kill all these suitors, because by then it will probably be about time for some sweet revenge.
As Mentes leaves, Telemachos tries to offer him gifts, as well as a bath and bed for the night, but Mentes politely declines.
Then, Athene fills Telemachos with a vision of his father. He realizes that he was in the presence of a divine spirit, but he still doesn't know it was Athene.
Now it's about time for some music, so Phemios the bard sings about the Trojan War.
This is rather an insensitive choice of subject matter, since the elephant in the room is that Odysseus's absence is probably the result of his dying in the Trojan War.
Penelope, who obviously agrees with our "insensitive" label, comes down from her room to politely request that he sing another song, preferably not one about her most likely dead husband.
Telemachos reproaches his mother and allows Phemios to keep singing.
Actually, Telemachos quite rationally explains that it's not the poet's fault Odysseus hasn't come home. Obviously it's Zeus's fault.
Besides, lots of other families lost their men in the war, and you don't see them running around crying their heads off.
Penelope is struck by Telemachos's wisdom (callousness?) and goes back upstairs to sleep. Take that, mom!
Telemachos, flush from victory over his grieving mom and still high with courage from his visit with the divine, tells the suitors that they have to leave at dawn.
Antinoös, one of the suitors, protests. He claims that Ithaka needs a king (like maybe … Telemachos?) and that the suitors are here to provide one.
Eurymachos, another suitor, asks who the stranger was and if he brought any news of Odysseus.
Telemachos lies and says that the visitor was Mentes and then heads up to bed, where the nurse Eurykleia, who was the servant of Laertes, Odysseus's father, takes care of him.