Homer uses foreshadowing to build anticipation and tension throughout the story. Because this tale was originally told orally, Homer had to keep the audience entertained and paying attention to the story by using literary devices like foreshadowing and dramatic irony.
"the worst fate you can think of..."See in text(Book I)
This functions as both a question and a challenge. Telemachus knows very well that all the suitors would like him out of the picture and that they would, if given the opportunity, kill him themselves. It's possible they're already plotting against him. That Telemachus says this and that he goes on to say he'd like to be chief, like his father, indicates that he's coming into his own power.
This declaration, so obviously a lie, tells the reader that Athena's guesses about Odysseus' whereabouts are in fact true and that he will be taken hostage by a group of savages, but since we haven't seen this yet, we can assume Homer is foreshadowing something he'll relate to us later in the poem.
A bearing-post "bears" the weight of a building and is essential to its structure. It recalls the image of Atlas, who bears the weight of the heavenly spheres on his shoulder, and foreshadows a more significant bearing-post that Homer will reveal later in the poem.
These opening passages function like a summary of what lies ahead in this epic poem. We haven't seen Odysseus with the nymph Calypso, nor have we seen the Greek gods decide to free him, but all of these things will come to pass. In that sense, these lines foreshadow the events to come.
"Odysseus may come back after all..."See in text(Book III)
Nestor’s question foreshadows Odysseus triumphant return at the end of the poem. Homer frequently foreshadows key moments, hinting at what’s to come, to build suspense.
"some god who was exactly like him..."See in text(Book IV)
It was fairly common for gods to take the form of humans, and the suitors would be familiar with this phenomenon. However, for them to assume that Telemachus was being helped by a god, they would necessarily have to think that he's in the right and that their position is in danger. We'll see how this plays out later.
"but they did not know what was going to happen..."See in text(Book IV)
Homer is pointing out that the Fates have already determined the outcome of the struggle between Penelope's suitors and Odysseus. Nothing they do can change the outcome, and even the gods cannot significantly alter the outcome.
"I should like my future husband to be just such another as he is..."See in text(Book VI)
Nausicaa states that she wants a future husband to be just like Odysseus; however, it is clear that she already prefers him to any other potential suitors as an ideal mate. Homer uses Nausicaa's statement here to foreshadow a serious relationship between Nausicaa and Odysseus.
"absolutely without any name whatever..."See in text(Book VIII)
A clever act of foreshadowing on Homer's part. In the next book of the poem, we will see an instance in which not having a name (or being "no one") will make the difference between life and death for Odysseus. This idea of being nameless ties into the theme of identity, which the Greeks based on one's social status and physical strength.
"I am always the first to bring a man down with my arrow..."See in text(Book VIII)
Homer uses foreshadowing here to build the audience's anticipation and hint at the events to come. Odysseus' prowess as an archer was well-known throughout Greece and Troy and would've been part of the stories told about him. In that sense, Odysseus is giving himself away through his boasting.
"poplars and willows that shed their fruit untimely..."See in text(Book X)
Since poplars and willows are commonly found around graves, this is a reference to death as an untimely occurrence as well as a landmark for Odysseus on his journey.
"All that I have said will come true..."See in text(Book XI)
Remember that Tiresias has presented Odysseus with two options: he can either take the easy way or the hard way. It's impossible for him to do both, suggesting that what Tiresias actually refers to here is the second, longer option of Odysseus fighting his way home after a very long journey.
"if you can restrain yourself..."See in text(Book XI)
Moderation in indulging one's tastes and desires is one of the central Greek virtues. If Odysseus' men can withstand hunger, Tiresias says, they will make it home safely. This also foreshadows events in Book XII, in which Odysseus "restrains" himself while listening to the song of the Sirens.
This is the home island of Helios (also, Apollo), the sun god. In Book I of The Odyssey, Homer told us that Odysseus' men had slaughtered Apollo's cattle and been punished, so we know even before Tiresias completes his prophecy that this is true and will come to pass shortly.
"you will return late, in bad plight, after losing all your men..."See in text(Book XII)
This outcome, by the way, has already been foretold by the prophet Teiresias when Odysseus sought him out in Hades. The repetition of this information benefits the oral narrator and the readers by helping to provide structure to the story.
"carrying one who was as cunning as the gods..."See in text(Book XIII)
Homer may be purposefully foreshadowing the events that take place when Odysseus arrives home. In Ithaca, his chief strengths will be his quick thinking and adaptability.
Theoclymenus has appeared at exactly the right time in the narrative. His prophecies help bolster Telemachus' confidence, which has been waning without proof of his father's return, and foreshadows the final books of the poem, when Telemachus finally faces the suitors.
"an eagle with a great white goose..."See in text(Book XV)
A powerful omen that Odysseus has indeed returned to Ithaca and will soon have the false suitors at his mercy. In Book II, Telemachus saw a similar omen during the meeting of the councillors when two great eagles sent by Zeus stared down at Telemachus's enemies, as if warning them not to cross him.
"I wish I were as young as you are..."See in text(Book XVI)
Notice how Odysseus declares what he would do were he in Telemachus's shoes. In doing so, Odysseus not only foreshadows his own triumph, but he also uses this as an opportunity to stir up his son's anger.
"eagles or vultures with crooked talons..."See in text(Book XVI)
Homer consciously chooses this simile comparing them to of birds of prey to foreshadow what Odysseus and Telemachus become when they confront the suitors.
Homer arranges it so that Euryclea sees Telemachus first to emphasize her close relationship with Telemachus and his family. As Nurse, she has been Telemachus' primary caregiver and thus the one most likely to support him. This also foreshadows her later recognition of Odysseus.
"by one of the bearing-posts..."See in text(Book XVII)
Interestingly, this isn't the first time Penelope has been mentioned as being by a "bearing-post" of the house. As before, this can be taken as a sign that she needs to feel some kind of support in this tense atmosphere. It's also foreshadowing of a scene later in the poem.
"Odysseus will return in this self same year; with the end of this moon and the beginning of the next he will be here..."See in text(Book XIX)
While this oath doesn't appear to have impressed Penelope very much, Odysseus is still irrevocably committing himself to his plan for revenge by calling upon Zeus to witness it. As to the timing Odysseus mentions, most scholars believe that Odysseus plans his return and revenge on Apollo's (god of the bow) feast day, which is the end of the month.
"this bow shall take the life and soul out of many a chief among us..."See in text(Book XXI)
This is an example of foreshadowing, in the sense that the suitors will be unsuccessful, but, in the original Greek, the sense of this line is that the bow will defeat the spirits of the suitors, not "take the life" as this translation states.