With many books, translations are negligible, with two obvious exceptions, one is the Bible, and surprisingly the other is The Iliad. Each translation can give a different insight and feel to the story. Everyone will have a favorite. I have several.
"Rage--Goddess, sing the rage of Peleus' son Achilles, Murderous, doomed, that cost the Achaeans countless losses, hurling down to the House of Death so many souls, great fighters' souls. But made their bodies carrion, feasts for dogs and birds, and the will of Zeus was moving towards its end. Begin, Muse, when the two first broke and clashed, Agamemnon lord of men and brilliant Achilles." -Translated by Robert Fagles, 1990
"Sing, O Goddess, the anger of Achilles, son of Peleus, that brought countless ills upon the Achaeans. Many a brave soul did it send hurrying down to Hades, and many a heroes did it yield a prey to dogs and vultures for so were the counsels of Zeus fulfilled from the day on which the son of Atreus, king of men, and great Achilles first fell out with one another." -Translated by Samuel Butler, 1888
"Rage: Sing, Goddess, Achilles' rage, Black and murderous, that cost the Greeks Incalculable pain pitched countless souls Of heroes into Hades' dark, And let their bodies rot as feasts For dogs and birds, as Zeus' will was done. Begin with the clash between Agamemnon-- The Greek Warlord--and godlike Achilles." -Translated by Stanley Lombardo, 1997
"Anger be now your song, immortal one, Akhilleus' anger, doomed and ruinous, that caused the Akhaians loss on bitter loss and crowded brave souls into the undergloom, leaving so many dead men--carrion for dogs and birds; and the will of Zeus was done. Begin it when the two men first contending broke with one another-- the Lord Marshal Agamémnon, Atreus' son, and Prince Akhilleus." -Translated by Translated by Robert Fitzgerald, 1963
"Sing, goddess, the anger of Peleus' son of Achilleus and its devastation, which puts pains thousandfold upon the Achains, hurled in the multitudes to the house of Hades strong souls of heroes, but gave their bodies to be the delicate feasting of dogs, of all birds, and the will of Zeus was accomplished since that time when first there stood the division of conflict Atrecus' son the lord of men and brilliant Achilleus." -Translated by Richmond Lattimore, 1951
"Sing, goddess, of Peleus' son Achilles' anger, ruinous, that caused the Greeks untold ordeals, consigned to Hades countless valiant souls, heroes, and left their bodies prey for dogs or feast for vultures. Zeus's will was done from when those two first quarreled and split apart, the king, Agamemnon, and matchless Achilles." -Translated by Herbert Jordan, 2008
"An angry man-there is my story: the bitter rancor of Achillês, prince of the house of Peleus, which brought a thousand troubles upon the Achaian host. Many a strong soul it sent down to Hadês, and left the heroes themselves a prey to the dogs and carrion birds, while the will of God moved on to fulfillment." -Translated and transliterated by W.H.D. Rouse, 1950
"Achilles' wrath, to Greece the direful spring Of woes unnumber'd, heavenly goddess, sing! That wrath which hurl'd to Pluto's gloomy reign The souls of mighty chiefs untimely slain; Whose limbs unburied on the naked shore, Devouring dogs and hungry vultures tore. Since great Achilles and Atrides strove, Such was the sovereign doom, and such the will of Jove!" -Translated by Alexander Pope, 1720
"Achilles sing, O Goddess! Peleus' son; His wrath pernicious, who ten thousand woes Caused to Achaia's host, sent many a soul Illustrious into Ades premature, And Heroes gave (so stood the will of Jove) To dogs and to all ravening fowls a prey, When fierce dispute had separated once The noble Chief Achilles from the son Of Atreus, Agamemnon, King of men." -Translated by William Cowper, London 1791
"Achilles' baneful wrath - resound, O goddess - that impos'd Infinite sorrow on the Greeks, and the brave souls loos'd From beasts heroic; sent them far, to that invisible cave* That no light comforts; and their limbs to dogs and vultures gave: To all which Jove's will give effect; from whom the first strife begun Betwixt Atrides, king of men, and Thetis' godlike son*" -Translated by George Chapman, 1616
"The Rage of Achilles--sing it now, goddess, sing through me the deadly rage that caused the Achaeans such grief and hurled down to Hades the souls of so many fighters, leaving their naked flesh to be eaten by dogs and carrion birds, as the will of Zeus was accomplished. Begin at the time when bitter words first divided that king of men, Agamemnon, and godlike Achilles." -Translated by Stephen Mitchell
"Sing now, goddess, the wrath of Achilles the scion of Peleus, ruinous rage which brought the Achaians uncounted afflictions; many of the powerful souls it sent to the dwelling of Hades, those of the heroes, and spoil for the dogs it made it their bodies, plunder for the birds, and the purpose of Zeus was accomplished__" -Translated by Rodney Merrill
"Sing, goddess, the anger of Achilles, Peleus' son, the accused anger which brought the Achaeans countless agonies and hurled many mighty shades of heroes into Hades, causing them to become the prey of dogs and all kinds of birds; and the plan of Zeus was fulfilled." -Translated by Anthony Verity
"Of Peleus' son, Achilles, sing, O Muse, The vengeance, deep and deadly; whence to Greece Unnumbered ills arose; which many a soul Of mighty warriors to the viewless shades Ultimately sent; they on the battle plain Unburied lay, to rav'ning dogs, And carrion birds; but had Jove decreed," -Translated by Edward Smith-Stanly 1862
"Sing, Goddess of the rage of Achilles, son of Peleus- that murderous anger witch condemned Achaeans to countless agonies and threw many warrior souls deep into Hades, leaving their dead bodies carrion food for dogs and birds- all in the fulfillment of the will of Zeus" - Translated by Professor Ian Johnston, British Columbia 2006
"The rage, sing O goddess, of Achilles, son of Peleus, The destructive anger that brought ten-thousand pains to the Achaeans and sent many brave souls of fighting men to the house of Hades and made their bodies a feast for dogs and all kinds of birds. For such was the will of Zeus." - Translated by Barry B. Powell
Another translation is by Ennis Samuel Rees, Jr. (March 17, 1925 - March 24, 2009)
You will find that some translations are easier to read but others are easier to listen to on recordings, lectures, Kindle, and the like. If you do not see information on specific translators, it is still worth the speculation and purchase. Right after the translation readability and understanding, do not overlook the introduction which gives an inset to what you are about to read.
The Stephen Mitchell translation goes though each of the major characters so well that you think you know them before you starts reading. Other introductions explain the struggle between different types of power. Rodney Merrill's 28 page introduction focuses on singing.
The Oxford University Press Barry B. Powell has an extensive introduction with real "MAPS". Also there is information of the finder Schliemann. We even get annotation on the meaning being conveyed.
Our story takes place in the ninth year of the ongoing war. We get some introduction to the first nine years but they are just a background to this tale of pride, sorrow and revenge. The story will also end abruptly before the end of the war.
We have the wide conflict between the Trojans and Achaeans over a matter of pride; the gods get to take sides and many times direct spears and shields.
Although the more focused conflict is the power struggle between two different types of power. That of Achilles, son of Peleus and the greatest individual warrior and that of Agamemnon, lord of men, whose power comes form position.
We are treated to a blow by blow inside story as to what each is thinking and an unvarnished description of the perils of war and the search for Arête (to be more like Aries, God of War.)