Nostos (νόστος, "homecoming") occurs seven times in the poem. Thematically, the concept of homecoming is much explored in Ancient Greek literature, especially in the post-war homeward fortunes experienced by the Atreidae (Agamemnon and Menelaus), and Odysseus (see the Odyssey). Thus, nostos is impossible without sacking Troy—King Agamemnon's motive for winning, at any cost.
Kleos (κλέος, "glory, fame") is the concept of glory earned in heroic battle. For most of the Greek invaders of Troy, notably Odysseus, kleos is earned in a victorious nostos (homecoming). Yet, Achilles must choose only one of the two rewards, either nostos or kleos. In Book IX (IX.410–16), he poignantly tells Agamemnon's envoys—Odysseus, Phoenix, Ajax—begging his reinstatement to battle about having to choose between two fates (διχθαδίας κήρας, 9.411).
The passage reads (the translation is Lattimore's):
μήτηρ γάρ τέ μέ φησι θεὰ Θέτις ἀργυρόπεζα (410) διχθαδίας κῆρας φερέμεν θανάτοιο τέλος δέ. εἰ μέν κ’ αὖθι μένων Τρώων πόλιν ἀμφιμάχωμαι, ὤλετο μέν μοι νόστος, ἀτὰρ κλέος ἄφθιτον ἔσται εἰ δέ κεν οἴκαδ’ ἵκωμι φίλην ἐς πατρίδα γαῖαν, ὤλετό μοι κλέος ἐσθλόν, ἐπὶ δηρὸν δέ μοι αἰὼν (415) ἔσσεται, οὐδέ κέ μ’ ὦκα τέλος θανάτοιο κιχείη.
For my mother Thetis the goddess of silver feet tells me I carry two sorts of destiny toward the day of my death. Either, if I stay here and fight beside the city of the Trojans, my return home is gone, but my glory shall be everlasting; but if I return home to the beloved land of my fathers, the excellence of my glory is gone, but there will be a long life left for me, and my end in death will not come to me quickly.
In forgoing his nostos, he will earn the greater reward of kleos aphthiton (κλέος ἄφθιτον, "fame imperishable"). In the poem, aphthiton (ἄφθιτον, "imperishable") occurs five other times, each occurrence denotes an object: Agamemnon's sceptre, the wheel of Hebe's chariot, the house of Poseidon, the throne of Zeus, the house of Hephaestus. Translator Lattimore renders kleos aphthiton as forever immortal and as forever imperishable—connoting Achilles's mortality by underscoring his greater reward in returning to battle Troy.
Achilles' shield, crafted by Hephaestus and given to him by his mother Thetis, bears an image of stars in the centre. The stars conjure profound images of the place of a single man, no matter how heroic, in the perspective of the entire cosmos.
Akin to kleos is timê (τιμή, "respect, honor"), the concept denoting the respectability an honorable man accrues with accomplishment (cultural, political, martial), per his station in life. In Book I, the Greek troubles begin with King Agamemnon's dishonorable, unkingly behavior—first, by threatening the priest Chryses (1.11), then, by aggravating them in disrespecting Achilles, by confiscating Briseis from him (1.171). The warrior's consequent rancor against the dishonorable king ruins the Greek military cause.
The poem's initial word, μῆνιν (mēnin, accusative of μῆνις, mēnis, "wrath, rage, fury"), establishes the Iliad's principal theme: The "Wrath of Achilles". His personal rage and wounded soldier's vanity propel the story: the Greeks' faltering in battle, the slayings of Patroclus and Hector, and the fall of Troy. In Book I, the Wrath of Achilles first emerges in the Achilles-convoked meeting, between the Greek kings and the seer Calchas. King Agamemnon dishonours Chryses, the Trojan priest of Apollo, by refusing with a threat the restitution of his daughter, Chryseis—despite the proffered ransom of "gifts beyond count". The insulted priest prays his god's help, and a nine-day rain of divine plague arrows falls upon the Greeks. Moreover, in that meeting, Achilles accuses Agamemnon of being "greediest for gain of all men". To that, Agamemnon replies:
But here is my threat to you. Even as Phoibos Apollo is taking away my Chryseis. I shall convey her back in my own ship, with my own followers; but I shall take the fair-cheeked Briseis, your prize, I myself going to your shelter, that you may learn well how much greater I am than you, and another man may shrink back from likening himself to me and contending against me.
After that, only Athena stays Achilles's wrath. He vows to never again obey orders from Agamemnon. Furious, Achilles cries to his mother, Thetis, who persuades Zeus's divine intervention—favouring the Trojans—until Achilles's rights are restored. Meanwhile, Hector leads the Trojans to almost pushing the Greeks back to the sea (Book XII). Later, Agamemnon contemplates defeat and retreat to Greece (Book XIV). Again, the Wrath of Achilles turns the war's tide in seeking vengeance when Hector kills Patroclus. Aggrieved, Achilles tears his hair and dirties his face. Thetis comforts her mourning son, who tells her:
So it was here that the lord of men Agamemnon angered me. Still, we will let all this be a thing of the past, and for all our sorrow beat down by force the anger deeply within us. Now I shall go, to overtake that killer of a dear life, Hektor; then I will accept my own death, at whatever time Zeus wishes to bring it about, and the other immortals.
Accepting the prospect of death as fair price for avenging Patroclus, he returns to battle, dooming Hector and Troy, thrice chasing him 'round the Trojan walls, before slaying him, then dragging the corpse behind his chariot, back to camp.
Fate (κήρ, kēr, "fated death") propels most of the events of the Iliad. Once set, gods and men abide it, neither truly able nor willing to contest it. How fate is set is unknown, but it is told by the Fates and by Zeus through sending omens to seers such as Calchas. Men and their gods continually speak of heroic acceptance and cowardly avoidance of one's slated fate. Fate does not determine every action, incident, and occurrence, but it does determine the outcome of life—before killing him, Hector calls Patroclus a fool for cowardly avoidance of his fate, by attempting his defeat; Patroclus retorts: 
No, deadly destiny, with the son of Leto, has killed me, and of men it was Euphorbos; you are only my third slayer. And put away in your heart this other thing that I tell you. You yourself are not one who shall live long, but now already death and powerful destiny are standing beside you, to go down under the hands of Aiakos' great son, Achilleus.
Here, Patroclus alludes to fated death by Hector's hand, and Hector's fated death by Achilles's hand. Each accepts the outcome of his life, yet, no-one knows if the gods can alter fate. The first instance of this doubt occurs in Book XVI. Seeing Patroclus about to kill Sarpedon, his mortal son, Zeus says:
Ah me, that it is destined that the dearest of men, Sarpedon, must go down under the hands of Menoitios' son Patroclus.
About his dilemma, Hera asks Zeus:
Majesty, son of Kronos, what sort of thing have you spoken? Do you wish to bring back a man who is mortal, one long since doomed by his destiny, from ill-sounding death and release him? Do it, then; but not all the rest of us gods shall approve you.
In deciding between losing a son or abiding fate, Zeus, King of the Gods, allows it. This motif recurs when he considers sparing Hector, whom he loves and respects. Again, Hera asks him:
Father of the shining bolt, dark misted, what is this you said? Do you wish to bring back a man who is mortal, one long since doomed by his destiny, from ill-sounding death and release him? Do it, then; but not all the rest of us gods shall approve you.
Again, Zeus appears capable of altering fate, but does not, deciding instead to abide set outcomes; yet, contrariwise, fate spares Aeneas, after Apollo convinces the over-matched Trojan to fight Achilles. Poseidon cautiously speaks:
But come, let us ourselves get him away from death, for fear the son of Kronos may be angered if now Achilleus kills this man. It is destined that he shall be the survivor, that the generation of Dardanos shall not die ...
Divinely aided, Aeneas escapes the wrath of Achilles and survives the Trojan War. Whether or not the gods can alter fate, they do abide it, despite its countering their human allegiances; thus, the mysterious origin of fate is a power beyond the gods. Fate implies the primeval, tripartite division of the world that Zeus, Poseidon, and Hades effected in deposing their father, Cronus, for its dominion. Zeus took the Air and the Sky, Poseidon the Waters, and Hades the Underworld, the land of the dead—yet they share dominion of the Earth. Despite the earthly powers of the Olympic gods, only the Three Fates set the destiny of Man.
The Male Totem
Recently it was proposed that in the Iliad Homer looked into the soul of man the warrior. 'Kleos' and warrior interrelations are viewed through anthropological, ethnological animistic concepts.
"the Iliad is a poetical rendition of male phyletic fantasies. The Iliad is about ‘klea andron’, the glorious and terrible deeds of men in relation to other men, the raw content of the soul of man, but not of woman. It is a vast lagoon of dream fragments of the male unconscious, haunted with eternal shadows that compete, strut, fight, kill and rape, and above all seek the approval of other men.”