If by part you mean Book, then you are partially correct. Odyseus is mentioned, certainly (an allusion by the goddess Athena), but the main characters are the goddess and Odyseus's son, Telemachus.
Telemachus is at home when Athena comes to him and gives him information about his father being alive. She doesn't say in so many words, Odyseus being still out of favor with several gods after the Fall of Troy and his persecution at the hands of Neptune:
The rest, all those who had perdition ’scaped
By war or on the Deep, dwelt now at home;
Him only, of his country and his wife
Alike desirous, in her hollow grots
Calypso, Goddess beautiful, detained
Wooing him to her arms. But when, at length,
(Many a long year elapsed) the year arrived
Of his return (by the decree of heav’n)
To Ithaca, not even then had he,
Although surrounded by his people, reach’d
The period of his suff’rings and his toils.
Yet all the Gods, with pity moved, beheld
His woes, save Neptune; He alone with wrath
Unceasing and implacable pursued
Godlike Ulysses to his native shores.
(Taken from William Cowper's translation)
Book I focuses mainly on the homefront since the end of the Trojan War and Odyseus's attempts to come home.
Influence with the gods.