WITH Funeral Games, Mary Renault closes her trilogy of novels about Alexander the Great. It follows Fire from Heaven (1969), which narrated his boyhood and youth, his relations with his parents-- coarse, efficient Philip and the barbaric, half-mad Olympias--and his assumption of the kingship of his native Macedon. The Persian Boy (1972) is the account of his conquest of most of the then-known world, first the Persia of Darius, then Egypt, and then all of Asia to the gates of India. As Funeral Games opens, he lies dying in the palace at Babylon.

The title is an irony. Alexander had been shaped in part by his devotion to the world of the Homeric epics. His own death, however, is not commemorated in the elaborate, ritualized games by which the Homeric heroes were mourned. Instead, his empire falls apart, and claimants battle each other for his legacy. He is therefore at once an ancient and a modern hero. Ancient because he founded an empire which is to us antique, remote. Modern because he was moved by ideals of conduct which had become anachronistic.

The trilogy is an extraordinary achievement, its parts echoing and re-echoing, themes twining, images and gestures of character repeating themselves. The titles offer evidence of this. Thus, in the first novel, Alexander's vaulting ambition, his sense of himself as a being set apart for a special destiny is nourished by his mother, who hints to him that he is not the son of Philip, but of a god, perhaps Zeus or perhaps Herakles, the mortal who became a god. In the second novel, he travels to the remote desert oracle of Zeus-Ammon at Siwa, to seek confirmation of this, and hence of his destiny. But it is in the final novel, with Alexander dead and Olympias grown old but no less murderous, that we understand the meaning of the fire from heaven which may have descended upon her.

Gore Vidal has described this Alexandriad as "one of the century's most unexpectedly original works of art." Their originality might be suggested by a comparison with Vidal's own fictional reconstructions of the ancient world, which are witty, Shavian in their serious high spirits, crammed with ironies of intelligence, urbane, deliberately playful. Renault has a similarly civilized response to history, but she has something other and more astonishing in view.

From early on, certainly from The King Must Die, it has been clear that her concern is with those episodes, historical or mythological or half-history and half- myth, which have left a residue within the mind of Western man, which have shaped our collective imagination of our past. She tells stories which we already half-know, and we half-know them because they exist somewhere within the forest of our imaginations as a cultural, almost as a biological inheritance. The story of Theseus, which she retold in earlier novels, is the story of the birth of civilization, a myth of the birth of our world embodied in images which have the contours of the imagination itself. The myth of Alexander has a similar existence in psychic time.

Encyclopedias and history books of the old-fashioned kind divide his story in two. First his life, so far as that can be known: there are no contemporary records, and historians must rely upon chronicles set down three or four centuries after his death in 323 B.C. And then what the Britannica calls "the Romance of Alexander," the great saga-like body of legend and myth which began during his lifetime and grew over the centuries and across the world from Gaul to India. In Egypt, the legends drew to themselves elements from the ancient epic of Gilgamesh. In Persia he became Iskander, a son of Darius. He was one of the great heroes invoked in the Gaelic poetry written in Ireland in the 18th century. The power which forced those legends into being is one of the subjects of Funeral Games. In death, Alexander dominates his world, evidence that something extraordinary had happened, that never again would men live with their old notions of the limits of ambition.

Renault is a supremely artful writer-- too artful, some might say, her technique at times wilfully, flamboyantly precious. She weighs probabilities, as an historian must when dealing with half-legendary material. But she knows that the material which she handles must be turned into art, and indeed into a specifically contemporary art. She has no time for pastiche, or for the sentimentalization of the past.

Technique is her instrument of transformation. Each of the three novels deliberately sets itself a formidable technical problem, and then solves it in a dazzling manner. In Fire from Heaven, it is the task of displaying not the accomplishments of a world conqueror, but his boyhood, creating his moral nature by deploying the contrasting natures and meanings of Philip and Olympias, who present what will become the warring aspects of his being--the hard-headed, shrewd tactician, and the mad, God-inspired dreamer, a somnambulist of power. In The Persian Boy she must show us a hero conquering Asia and becoming Asiatic in the process, a leather-tough Macedonian adrift among odors, music, and splendor. And this she does by inventing (or almost inventing) as her narrator Bagoas, the beautiful Persian male courtesan who becomes Alexander's lover. Now, in Funeral Games, she has set herself the task of inventing a novel which opens with the death of its central figure.

Technique, however, is in all three instances not a distraction from subject and theme, but rather their precise embodiment. In Funeral Games, she is concerned not now with Alexander's nature, but rather with his mystery, with the power which, beyond death, exerted itself first upon those who survived him, and then upon the imagination of history. In this way, she has not taught us a history lesson, but instead has drawn us back to a past of which we were ignorant only because we had forgotten. Perhaps what she has created in us is an illusion, but it is one of those strong, lovely, nourishing illusions of which art alone is capable.