First, the Sparknotes summary:
Athena travels to Sparta, where she finds Telemachus and Pisistratus, Nestor’s son. She tells Telemachus he must hurry home to Ithaca before the suitors succeed in winning his mother’s hand. She also warns him of the ambush that they have set and explains how to avoid it. Finally, she instructs him to head first for the home of the swineherd Eumaeus, who will convey the news of his safe return to Penelope.
The next day, Telemachus announces his departure and accepts gifts from Menelaus and Helen. As Telemachus pulls away from the palace in his chariot, an eagle carrying a goose stolen from a pen swoops down beside him. Helen interprets the incident as an omen that Odysseus is about to swoop down on his home and exact revenge on the suitors.
Once at Pylos, Telemachus has Pisistratus drop him off at his ship, insisting that he has no time to spare to visit Nestor again. The ship is about to set off when Theoclymenus, a famous prophet’s descendant who is fleeing prosecution for a crime of manslaughter that he committed in Argos, approaches Telemachus and asks to come aboard. Telemachus welcomes him and offers him hospitality when they get to Ithaca.
In the hut of Eumaeus, Odysseus tests the limit of his hospitality by offering to leave in the morning, a false gesture that he hopes will prompt Eumaeus to offer to let him stay longer. He urges the old man not to go out of his way and says that he will earn his keep working for the suitors, but Eumaeus will have none of it. To get mixed up with those suitors, he warns, would be suicide. Odysseus and the swineherd then swap stories. Eumaeus explains how he first came to Ithaca: the son of a king, he was stolen from his house by Phoenician pirates with the help of a maid that his father employed. The pirates took him all over the seas until Laertes, Odysseus’s father, bought him in Ithaca. There, Laertes’ wife brought him up alongside her own daughter, the youngest born.
The next morning, Telemachus reaches the shores of Ithaca. He disembarks while the crew heads to the city by ship. He entrusts Theoclymenus to a loyal crewman, Piraeus. As they part, they see a hawk fly by carrying a dove in its talons, which Theoclymenus interprets as a favorable sign of the strength of Odysseus’s house and line.
In this book, it is Telemakhos rather that Odysseus who is depicted as needing to make a return (nostos) to his home (oikos) and native land (patris gaia), assisted by Athene - another example of his attributes and conduct being drawn in parallel with those of his father.
Athene tells Telemakhos that there is a danger that Penelope will now marry one of the suitors and forget about him; and indeed, as we shall see, Penelope is close to giving in and agreeing to remarry. Telemakhos has the good sense to obey the goddess.
The world of the Odyssey is one in which the gods are at hand to provide help or hindrance to humans, and we are reminded in this Book that it is also one in which omens (two of them, in this case) can be used to divine the future, through the offices of seers like the somewhat enigmatic Theoklymenos.
It is noteworthy that Theoklymenos, on meeting Telemakhos, asks him to identify himself by means of his place of origin and his parents - an indication of the importance of place and parentage in the epic.
Eumaios's story of his life is illuminating. It appears that Eumaios is of noble blood, but he finds himself working as a slave among his master's pigs because he had the misfortune to be captured by Phoenician traders. In an epic which is largely set among high-born aristocrats, this serves as a reminder that social status is dependent as much on chance as anything else.
Finally, we see the recurrent motif of guest-friendship or hospitality, which is successively offered by Menelaus to Telemakhos, by Telemakhos to Theoklymenos and by Eumaios to Odysseus.