One of the main elements of Book I of the Odyssey is the conflict between the suitors who are infesting Odysseus's house, on one hand, and Telemachus and Penelope, on the other. At this point in the poem, Odysseus has been gone twenty years, and almost everyone assumes he has died on the journey home. The suitors spend their days eating and drinking, wasting Odysseus's household wealth, while they wait for Penelope to decide which suitor to marry. Although their ostensible goal is to marry Penelope, they are interested mainly in obtaining Odysseus's land and wealth by marrying Penelope. Penelope does her part in delaying the decision. She has told the suitors that she will make her decision when she has finished weaving a piece of cloth, but at night, she undoes the day's weaving. Telemachus, on the other hand, is too immature to challenge the suitors, most of whom are older than he is.
Athena, acting on Zeus's command that it is time for Odysseus to get home, visits Telemachus in the form of a trusted friend and counselor of Odysseus named Mentes. She encourages Telemachus to get rid of the suitors, and although he tries, he his over-ruled by the town council. More important, however, Athena tells Telemachus to go look for his father:
As for yourself, let me prevail upon you to take the best ship you can get, with a crew of twenty men, and go in quest of your father who has so long been missing. Someone may tell you something, or (and people often hear things in this way) some heaven-sent message may direct you (Book I. 130 and following).
This is the beginning of Telemachus's growth in Books I-IV from an insecure youth to a more mature young adult with some confidence in himself and the belief that his father is indeed alive and trying to return to Ithaca. He has felt utterly alone up to this point; now, with the help of Athena-Mentes, he has what is known as a "coming-of-age" experience. He is clearly in command of his ship and has a growing awareness that he has responsibilities that extend far beyond himself.
Athena is undoubtedly the most important character in Books I and II because she constantly encourages and guides Telemachus as he traverses unknown territory. When, in Book III, Telemachus meets Nestor, his confidence grows quickly because he is treated with the respect he did not have on Ithaca. By consulting with Athena, and watching Nestor and his family, Telemachus begins to feel confident in his ability to meet his father's friends on equal terms and, more important, learn as much as possible about what might have happened to Odysseus.
In Book IV, when Telemachus visits Menelaus to learn whether Menelaus has any news of Odysseus, Telemachus conducts himself with courtesy and discretion, behavior that impresses Menelaus:
“Your discretion, my friend,” answered Menelaus, “is beyond your years. It is plain you take after your father. One can soon see when a man is son to one whom heaven has blessed both as regards wife and offspring. (Book IV 147 and following)
Aside from his experience with Nestor, Telemachus has never been accorded such respect, and it is reasonable to argue that Telemachus's confidence has increased exponentially during his visits with Nestor and Menelaus. We get the sense that, whatever happens from this point on, Telemachus will conduct himself as we would expect from the son of Odysseus.
The narrative essentially leaves Telemachus's story here and moves briefly back to Ithaca and then to several books devoted to the adventures of Odysseus.