Although the first sentence (using Samuel Butler's translation) of the Odyssey--
Tell me, O muse, of that ingenious hero who travelled far and wide after he had sacked the famous town of Troy--
provides part of the framework for Homer's narrative, it is hardly sufficient to indicate the scope of Odysseus and his men's journey back to Ithaca. The second sentence, however, arguably supplies a bare, but sufficient, outline of the return voyage:
Many cities did he visit, and many were the nations with whose manners and customs he was acquainted; moreover he suffered much by sea while trying to save his own life and bring his men safely home; but do what he might he could not save his men, for they perished through their own sheer folly in eating the cattle of the Sun-god Hyperion; so the god prevented them from ever reaching home.
This sentence effectively summarizes the number and variety of cultures Odysseus and his men encounter--the Lotus-Eaters, the Cyclops, Circe, Aiolus, the island of Hyperion--and the very important fact that Odysseus' men did not reach Ithaca.
Perhaps more important than anything is the statement that the men fail to reach home "through their own folly." When Odysseus and his men encounter the Lotus-Eaters, for example, several become so dulled by eating lotus leaves that they lose all interest in returning home, and Odysseus has to force them back onto the ships to save them from their own folly. Likewise, when Aiolus gives them a bag of winds to aid their voyage home, Odysseus' men disobey orders and open the bag, and the winds send them far off course. Finally, when they reach the island of Hyperion, the men's hunger and greed overcomes the warning not to eat Hyperion's cattle, and, after another in a long line of storms, Odysseus' men perish, leaving him to continue the voyage.
The first sentence, then, introduces the narrative, but the first two sentences combined frame Homer's narrative so that we are prepared for a number of struggles for both Odysseus and his crew. The second sentence, which provides specific details, also points to crucial information about Odysseus and the fate of Odysseus' men. As their king, under normal circumstances, Odysseus would be expected to care for his men so as to insure their survival. As Homer indicates, however, their failure to survive is not the result of Odysseus' carelessness but to the men's folly. Odysseus fails to bring his men home, an important duty, but this failure is clearly not his personal failure. His status as king, which will become very important once he reaches Ithaca, is still intact.
Homer clearly perceives Odysseus' duty to bring his men home safely as at least as important as getting himself back to Ithaca--note the amount of space in the second sentence given to Odysseus' men and the fact that they did not survive. The epic, even though Odysseus is at the center, is, in part, about the nature of kingship in the Bronze Age, as well as the weakness of men, and one can argue that the first two sentences successfully encapsulate the essence of the journey.