The book's profiles begin with Orpheus, the legendary father of poetry and music, whom Schmidt boldly treats as a real person: ''I take Orpheus to have been an actual man with an actual harp in his hand.'' After his wife, Eurydice, was lost in Hades, Orpheus turned to boy-love and was reputedly the first to practice it in his native Thrace. His death was gruesome: he was torn to bits by bacchants, and his severed head floated to the island of Lesbos, which was thereby impregnated with poetic genius.

Schmidt's chapters on Homer, while rich, seem too long for a survey book -- and we're still at the start of the ''Odyssey'' on the next-to-last page. Far more interesting than the excessive plot summary is Schmidt's treatment of Homeric diction as ''a composite of different dialect strands . . . as though a poet wrote in Scots, South African, Texan and Jamaican, all in a single poem.''

Much attention is devoted to controversies over the authorship of the ''Iliad'' and the ''Odyssey'': Was Homer a myth? Did one man (or even a woman) compose both poems? Was Homer merely a collator of inherited material? Schmidt makes Homer concrete by taking us on a lively fictionalized odyssey through his hypothetical life and experiences. As for those who allege there were two poets, Schmidt rightly scoffs, it's ''as though Shakespeare could not have written 'The Comedy of Errors' and 'Othello.' ''

To deny Homer's existence, Schmidt argues, ''impoverishes our reading.'' Regrettably, he doesn't joust with the notorious ''death of the author'' dogma of literary poststructuralism. He oddly fails to describe the classicist Milman Parry's pioneering use of recording technology to document survivals of the epic oral tradition in rural Yugoslavia in the 1930's. And he hurries past an influential 19th-century theory that a single bard, long after the Trojan War, wove heroic lays of military adventure into two integrated poems -- a process that would be repeated in medieval romances.

In his chapter on Hesiod, whose ''Works and Days'' and ''Theogony'' rivaled Homer's epics for near-biblical status in Greek culture, Schmidt gives glimmers of the more reader-friendly book that might have been -- an alluring, dreamlike travelogue of the Greek sites where ancient poets lived and created. ''Even today it is no easy matter, getting to where Hesiod's farm used to be,'' he says. Hiking through a parched landscape up Mount Helicon, he sees ''old olive trees clenched among the rock'' and is surprised by ''tiny gusts of exquisite scent'' from the ''wild, almost leafless cyclamen, pale dots of purple.''

With Archilochus, Schmidt hits his stride. ''The only Greek soldier-poet we have,'' Archilochus was born on wind-swept Paros, famed for its translucent marble. As a young man, he was leading a cow to market when the Muses appeared, stole the cow, and left a lyre in its place. Archilochus became a brazen sensualist, caustically irreverent. Schmidt calls him a ''cad,'' a cruel exploiter of women and ''an early defining figure of patriarchy''; his imagery has ''a reptilian eroticism.''

Alcman, who labored for Sparta, provides an eloquent contrast to cynical Archilochus. The ''I'' of Alcman's ''civic'' choral poetry was collective. Schmidt compares Alcman's work to masques like Milton's ''Comus,'' where poetry and music are interwoven. Alcman's poems were ''sung not in the intimacy of the symposium,'' a male dinner party, he writes, ''but in the open, public air.'' Schmidt also laments Sparta's cultural decline. Famous in the seventh century B.C. for its ''music, pottery and poetry,'' it became an imperial power so besotted by militarism that ''three centuries later, the adjective 'Spartan' had become synonymous with 'Philistine.' ''

Next we meet Mimnermus, whom Schmidt calls ''an elegist of pleasure,'' and the misogynous Semonides, who sees woman as sow, vixen and bitch. Then come the great poets of Lesbos, Alcaeus and Sappho, both aristocrats born during the politically unstable early seventh century. Schmidt calls Alcaeus ''a brilliant poet of wine'' and ''debauchery'' but also ''a survival poet, enduring exile and hardships.'' Ancient writers assumed he ''preferred the company of his own sex.''

In a substantial but uneven chapter on Sappho, Schmidt intriguingly speculates on where she was born and raised on Lesbos (a large island near the coast of Asia Minor): was it in the western village of Eressus in rough, barren country, or in the cosmopolitan eastern seaport of Mytilene? He subtly evokes her poetic style: ''Sappho's art is to dovetail, smooth and rub down, to avoid the over-emphatic.'' And he aptly compares the relationship between voice and musical accompaniment in Sappho's performance of her poems to the recitative in opera.

But although he acknowledges the way Sappho has ''appealed to the sexual prurience or moral severity of centuries of scholars and readers,'' Schmidt doesn't adequately summarize the passionate arguments over Sappho's character, public life and sexual orientation. He omits altogether the role played by the medieval church in burning her manuscripts. While Swinburne's darker rewriting of Sappho is quoted (with minimal comment), Catullus' far more important version receives only a passing mention. As for Sappho's two brilliantly original major poems, ''He Seems to Me a God'' receives less than a page of attention, and ''Ode to Aphrodite'' is barely glanced at. Instead, Schmidt wastes space with long, dreary quotes from a feminist classicist stuck on the usual dated ideology of male oppression.