John Updike explores what was really rotten in the first family of Denmark.

We tend to think of Shakespeare's Prince Hamlet as the first introvert of modern tragedy, with his theatrical domain - along with Wittenberg and rotten Denmark - as that of the first great Renaissance drama. But the prince's self-consciousness and madness, feigned or otherwise, couldn't by themselves give us the labyrinthine complexity of "Hamlet" - the brilliant ambiguities of the young man's soliloquies, the torturous sorrows of Ophelia's suicide, the play's explorations of good and evil and of humanity's moral obligation to understand both. With the ghost of Hamlet's dead father hovering over his son's conscience, we watch a tale unfold whose central action has already taken place: Claudius, King of Denmark and stepfather to the prince, has poisoned Hamlet's father and absconded with queen and crown. It will be Hamlet's role, of course, to unearth this lethal secret and then decide what to do about it. And while he spends the next five acts mostly thinking out loud, his meditations will end in a staggering last scene of consummate death.

Part of the play's timelessness lies in its dualities, about which volumes have been written, from the two dead kings to the collision between classical heroism and Reformation thought. This infinity of interpretation applies equally to the cast: Is Claudius really a vicious incorrigible, or has he straightened up since that Cain moment of weakness when he killed his brother? Is Queen Gertrude in fact a weak sister who sold out her only son, or is she an ermine-robed victim of ruthless patriarchy? And what of poor old Polonius? OK, so he's a self-serving bore and a hypocrite, both of which he pays for at the point of Hamlet's sword in the third act. But did any father ever love his daughter more?

And now, regarding the publication of "Gertrude and Claudius," dare one say it? What a piece of work is Updike! Our own king of erudition - a Renaissance writer if ever contemporary America could claim one - has gone back to the Hamlet story to imagine its inception: its offstage pre-story, when Claudius fell in love with his brother's queen and that first dastardly deed in the garden was set in motion. Wickedly replete with allusions, weaving the history of ideas with the lustier possibilities of adulterous coupling, "Gertrude and Claudius" is an intelligent little novel of whimsy. Opening with Gertrude's marriage, at 16, to King Hamlet, then following the building treachery of the next three decades, Updike's story ends with the stage set for the beginning of "Hamlet." It's the background case file, in other words, on the newlywed parents of the prince - their story exposed as a blended family in extremis, rife with the usual pitfalls of envy, boredom, and unleashed aggression.

You can feel Updike's pleasure and intellectual curiosity throughout this novel, for which he returned to several versions of the ancient Hamlet legend, in which Amleth, a Danish noble, takes revenge on his uncle for killing his father. Accordingly, Updike's characters are given the names drawn from Shakespeare's sources, including the 12th-century Latin text by Saxo Grammaticus and Francois de Belleforest's later adaptation in "Histoires tragiques." Thus Polonius appears as Corambis; Claudius as Feng and Fengon until he takes the reigning title of Claudius; and Gertrude as Gerutha, then Geruthe. This care has the added effect of making the story ageless as well as more intimate; in Updike's hands, at the story's lighter moments, what we have are a couple of unhappy campers who find their way into a second chance by way of each other's pre-silk undergarments.

Gertrude, in particular, is rendered with great sympathy. Deemed powerless by the men around her from the day she was born, she's cast here as a large-hearted, disappointed woman who must struggle to recognize her own desires. When Claudius gives her a blinded female falcon as a gift, he consoles Gertrude's worries: "It is for her own protection," he tells his beloved, "otherwise she will be frantic for the possibilities of freedom that she sees about her." Claudius hardly deserves such sympathy, roaming the Mediterranean and coveting his older brother's wife. But his passion for Gertrude is true, and the shadows of sibling rivalry that accompany it nonetheless coexist with a cosmopolitan, early-modern sensibility. By the time he enlists Polonius in that conspiracy to empty a vial of herbona into King Hamlet's ear, he has been pushed into desperation by circumstances of love as well as treachery.

Prince Hamlet himself is off in Wittenberg, naturally, reading philosophy in the place where Martin Luther nailed his "Theses" to the door. But the general discord he effects in "Gertrude and Claudius" would have us believe that this is a brooding boy who may turn out to be more trouble than joy: a "fragile, high-strung, quick-tongued child," his own mother thinks; she will come to believe that her son suffers from "the madness of detachment." None of which will slow Claudius in orchestrating the young man's return to Elsinore, of course - where Ophelia waits, Polonius plots, and Gertrude and Claudius happily reign.

The question at hand, though, is whether "Gertrude and Claudius" succeeds - as a self-contained story, a contemporary dramatic commentary, an elixir for the play itself. Well, yes, but only if you're keen to immerse yourself in "Hamlet" in order to partake of the pleasures Updike offers; otherwise, his reinterpretation may seem capricious or uninviting, as pedantic as Polonius to the uninitiated. The novel is written in prose correspondent to its history, which is authentic but hardly the stuff of Updike the splendid modern stylist. In an effort to place Gertrude and Claudius's love story in time, Updike has woven strains of intellectual history through the text - the rise of empiricism, say, or the collision between naturalism and the advent of Christianity. These strains worked for me; I can also imagine them seeming tedious to a reader in a less willing state of mind.

What seems luminescent about "Gertrude and Claudius" is its attendant passions - not those of the star-crossed, roguish lovers, but rather those authorial joys evoked by the tragedy of "Hamlet." There is something delightful about following Updike down this path, seeing his sentiments and sympathies unfold, watching him deftly handle the text of "Hamlet" and the spiritual ambiguities that surround it. Sometimes brilliant and sometimes thuddish, "Gertrude and Claudius" is an intellectual indulgence, but the indulgence is contagious. At its best, the novel will send you into the infinite luxuries of the play itself: its staircases of madness and wisdom, sorrow and pity. And so, in keeping with Updike's newfound heroine, we'll leave the final note of cunning to Queen Gertrude - who, when asked about her son's state of mind, replies, "Mad as the sea and wind when both contend / Which is the mightier." Give that woman a scepter!