All very common misconceptions.
Μῆνιν ἄειδε θεὰ Πηληϊάδεω Ἀχιλῆος
οὐλομένην, ἣ μυρί᾿ Ἀχαιοῖς ἄλγε᾿ ἔθηκε,
πολλὰς δ᾿ ἰφθίμους ψυχὰς Ἄϊδι προΐαψεν
ἡρώων, αὐτοὺς δὲ ἑλώρια τεῦχε κύνεσσιν
οἰωνοῖσί τε πᾶσι· Διὸς δ᾿ ἐτελείετο βουλή,
ἐξ οὗ δὴ τὰ πρῶτα διαστήτην ἐρίσαντε
Ἀτρεΐδης τε ἄναξ ἀνδρῶν καὶ δῖος Ἀχιλλεύς.
Goddess sing to us of anger, whereby Peleus' son Achilles,
ruined the Achaeans, without number, and fixed their pain,
were many stout souls to Hades, all heroes untimely sent,
their remains, the ready prize, of every dog and bird of prey,
this God fulfilled by design, yet not before quarrel set apart,
divine Achilles, and Atreus’ son, the master of upraised men.
Actually, the 24 books of the Iliad cover only about two weeks during the last year of the decade long war between the Trojans and Achaeans. It begins with Agamemnon’s seizure of Briseis, Achilles’ royal prize, his withdrawal from battle; and ends with the funeral of Hector. Telamonian-Ajax was not killed in the Iliad, rather therein he recovered the body of Patroclus, yet lost Achilles’ barrowed armour to Hector.
The death of Ajax was included in the Aethiopis and the Little Iliad, within the greater Trojan War Cycle, of which the Iliad is one part.
On the other hand...
ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ
πλάγχθη, ἐπεὶ Τροίης ἱερὸν πτολίεθρον ἔπερσεν·
πολλῶν δ᾽ ἀνθρώπων ἴδεν ἄστεα καὶ νόον ἔγνω,
πολλὰ δ᾽ ὅ γ᾽ ἐν πόντῳ πάθεν ἄλγεα ὃν κατὰ θυμόν,
ἀρνύμενος ἥν τε ψυχὴν καὶ νόστον ἑταίρων.
ἀλλ᾽ οὐδ᾽ ὣς ἑτάρους ἐρρύσατο, ἱέμενός περ·
αὐτῶν γὰρ σφετέρῃσιν ἀτασθαλίῃσιν ὄλοντο,
νήπιοι, οἳ κατὰ βοῦς Ὑπερίονος Ἠελίοιο
ἤσθιον· αὐτὰρ ὁ τοῖσιν ἀφείλετο νόστιμον ἦμαρ.
τῶν ἁμόθεν γε, θεά, θύγατερ Διός, εἰπὲ καὶ ἡμῖν.
Muse recall for us, the man much-travelled, of this most far and wide,
made to wonder, after the divine citadel of Troy was thrown asunder:
he beheld the men from many nations, and came to learn their minds,
indeed on the sea he suffered many pains, that caused his heart to fall,
from which he won for himself, his life and a fair wind homeward bound,
yet thusly he could not save his comrades, although this he did desire,
a reason provided, themselves for their bold sins, whereby they died,
not but children, whom the most-high Sun at noon put down as cows,
then consumed for after all, the day of their return had been deigned.
Indeed of this that follows, goddess, God's daughter, speak through me.
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These were as close to poetic English, that tries to capture the Homeric style, as I can come.
With the exceptions of an ill conceived attack on an Aegean island, a tour of the Levant, a raid on Egypt, and a quick trip to Denmark, the Odyssey mostly took place in the middle and western Mediterranean.
CmacQ
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