HOMER: THE ILIAD Translated by Robert Fagles Introduction and Notes by Bernard Knox Viking. 683 pp. $35

FOR MORE than a thousand years the most popular book in the Greek-speaking world was Homer's Iliad. It was studied and quoted in 5th-century Athens. It was recited to crowds from Asia Minor at the great festival of Apollo at Delos. Centuries afterwards in remote outposts, it was read eagerly and even translated by people who knew Greek only as a second language.

No single work of literature has had such a pervasive influence on other writing, since it was from the story of Achilles's anger and its deadly consequences that the notion of the "tragic flaw" ultimately derives. It was from Homer that students learned the basic patterns of rhetoric (Achilles is a fine speaker) and came to know about the capricious and dangerous character of their gods. And it was Homer too that provided young people with their first cruelly realistic impressions of the nature of human life.

Perhaps surprisingly for those who now imagine that dead white males can write only about their own "values," over the years Homer's many audiences included women, since women (like men) of the propertied classes learned to read and write. It was he who first portrayed them in their important role as survivors and the continuers of the culture that the men sought in their violence to destroy. It is Homer also who portrays the Greeks and their Trojan enemies with equal sympathy, and who shows that, ultimately, victors can suffer losses as great as the defeated in a war. As such The Iliad deserves to keep its place on the list of the books that every educated person ought to read.

Fortunately the reader has a choice among several modern English translations. For almost a generation there was no reasonable alternative to Richmond Lattimore's verse (1951), which kept remarkably close both to the tone and sense of the original. But Lattimore did not seek to scale down the length of Homer's lines or to interpret for his reader particularly foreign-sounding words or practices. Undergraduates of the 1980s quickly became discouraged. Robert Fitzgerald's shorter lines in his 1974 translation made the text easier to read, but still did not explain what the modern reader might need to know. Martin Hammond's accurate translation (1987) provides that information, but in deliberately formal prose. Robert Fagles now offers a verse translation that explains what readers need to know, in clear, vigorous language that still retains a sense of the sweep and the sonority of the original.

Here, first in Lattimore's translation, are a few lines (182-84) from Iliad IX, the "book" (or papyrus book-roll) that was most people's favorite in antiquity. Agamemnon, leader of the Greek army, has decided to apologize for the quarrel he started with Achilles, and to make amends for it. He sends ambassadors to Achilles, who in his anger has withdrawn from the fighting; these are Achilles's old tutor, Phoenix, and two of Achilles's friends, the great heroes Ajax (or in Greek, Aias) and Odysseus. So these two walked along the strand of the sea deep-thundering

with many prayers to the holder and shaker of the earth,

that they might readily persuade the great heart of Aiakides.

Lattimore reproduces in English the Homeric epithet for sea and inverts the word-order to give a sense of its traditional formality; he expects the reader to know that of these three Homer focuses on Odysseus and Ajax, and that the sea-god they pray to is Poseidon, and that Achilles is the descendant of the hero Aiakos.

In his translation of the same lines, Fitzgerald expands the epithet into a phrase and names the heroes: Following Phoenix,

Aias and Odysseus walked together

beside the tumbling clamorous whispering sea,

praying hard to the girdler of the islands

that they might easily sway their great friend's

heart.

But he does not explain which god is the "girdler of the islands" or give their great friend his name. Hammond's prose translation provides all the names but keeps the complex structure of the Greek sentence: "so they went along the shore of the sounding sea, praying long to Poseidon the encircler and shaker of the earth that it would be easy for them to win over the great heart of Achilleus, of Aiakos' stock."

Fagles's translation is still easier to understand because, by varying the length of the lines, he has space and time to expand the epithet, fill in the names, and simplify the grammar: So Ajax and Odysseus made their way at once

where the battle lines of breakers crash and drag,

praying hard to the god who moves and shakes the earth

that they might bring the proud heart of Achilles

round with speed and ease.

Because I know what the original says, I am more comfortable with Lattimore. But Fagles' translation will be far more accessible to non-specialists because it can be understood straight off. And the Fagles version also offers Bernard Knox's concise and informative introduction, which even Lattimore loyalists ought to read. Somehow Knox always manages to make the reader see how complex problems are important and interesting; his lucid discussion of the Homeric questions will be instructive to even the most jaded professional. Another plus: The Fagles translation (uniquely) has maps as well as glossaries and aids to pronunciation.

In his interpretation Knox places great emphasis on the critical differences between gods and men. For the gods -- ageless, powerful and immortal -- war is a game without lasting consequences; the gods can return to Olympus and leave human misery behind. But mortals, because they cannot escape death or time, achieve greatness through their awareness of their mortal limitations and suffering. Although Knox doesn't say much about the women of the Iliad, it is significant that the epic ends not on a note of triumph but with their lamentations at Hector's funeral. Like Hector and Achilles, Andromache, Hecuba, and even Helen live on in memory not for what they have won, but because of all that they have lost.

Mary Lefkowitz teaches classics at Wellesley College. Her most recent book is "Women in Greek Myth."