What is the function of Eumaeus the swineherd? How does he treat Odysseus, and how does Odysseus treat him? How much of the truth does Odysseus tell him?

Eumeus acts as the link between the island of Ithaca and the returned king Odysseus.

He treated Odysseus like any other guest, for he believes all guests are from Zeus and no one should be mistreated. Odysseus, on the other hand, put on a whole new identity and told false tales bout his upbringing and family.

Odysseus did not seem to reveal much about anything except for the fact that Odysseus will indeed return back to Ithaca and take care of the affairs and also of the suitors.

Explanation:

Eumeus is the linking factor of Odysseus and Ithaca. He was the first person to be approached by Odysseus on his return back to the island of Ithaca. He also serves as the shelter for Odysseus and his companion for his return to his palace and encounter the suitors.

When at first he was approached by Odysseus in his humble home, he treated him like any other guest. Providing him with change of clothes and food and drink, he even allowed him to spend the night and covered him with the warm animal skin to cover himself.

Odysseus also treated him like a host and asking him numerous questions about his master and the situation in the palace. He had been in disguise so it was easy for him to pretend like another person and not mislead the swineherd. Through Eumeus, Odysseus also came to know and plan his revenge on the suitors.

Odysseus, in his disguise, did not seem to reveal much about his own identity to Eumeus until all his plans had been successful. He lied about his identity and upbringing, but also stressed that Odysseus will indeed return and the swineherd should believe him and wait patiently for that moment.