I really wanted to like this book more than I did. It's clever, witty, imaginative and filled with ideas -- all things I prize in a book. And yet it lacks coherence, perhaps even a sense of full commitment by the author to his novel. I don't feel Banville's dedication to the material, a sense that he really had a compelling reason or desire to tell this story.

It is a kind of homage to the story of Amphytrion -- the mortal cuckolded by Zeus, who took Amphitryon's own shape to seduce his wife, Alcmene -- and to Kleist's play based on the story. And there is something theatrical about the setting -- an isolated country house where a family has gathered to wait for the death of the father, comatose after a stroke. The place is also haunted by the Greek gods -- Hermes keeps watch on things while his own father, Zeus, has his way with the beautiful actress wife (named, rather obviously, Helen) of the son of the dying man. Both son and father are named Adam, which only adds another layer of confusion to the story, which is narrated by Hermes, and then by the elder Adam in his comatose state, and then by both of them, blending and alternating until it's not clear who, other than Banville, is telling the story.

The elder Adam is a prominent intellectual -- a mathematician or a philosopher or a theoretical physicist -- whose ideas about infinity, or rather infinities, have changed the world: applications of his theories have led to automobiles that run on seawater. But the world in which the novel takes place is not our own: In this alternate world, for example, Mary, Queen of Scots, beheaded Elizabeth I, not the other way around. And Alfred Russel Wallace, not Darwin, was credited with the theory of evolution, which in any case has been disproved.

Yes, Banville is having fun, playing as much with Shakespeare (there is a character whose name, Wagstaff, is a translation of "Shakespeare") as with the classic myth or Kleist's version of it. Another character, Benny Grace, is both the god Pan and a version of Shakespeare's Puck, and the whole thing has a Midsummer Night's Dream quality to it. But the novel has a dark side, too: Old Adam's first wife drowned herself; his current wife, Ursula, is an alcoholic; their daughter, Petra, is a morbid young woman who is compiling a list of human ailments and secretly mutilates herself.

Is the problem with the novel that there is too much going on and not enough of it winds up anywhere meaningful? Perhaps. It's a verbal feast -- Banville is often compared to such word wizards as Nabokov and Joyce -- but I came away from it feeling a little queasy, as if I'd just been to a banquet of appetizers.