With some writers, interpretation seems like an impertinence; with others, it is a necessity; with a few – and these are perhaps the greatest – it is both at once. Franz Kafka is preeminent in this third category, welcoming paradox here as in every aspect of his work. Nothing could be truer to the spirit of Kafka – more Kafkan, one might say, to avoid the hackneyed and misleading “Kafkaesque” – than to write a book in response to his books, as Roberto Calasso has done in “K.” (Alfred A. Knopf, 327 pages, $25). Many of his stories take the form of parables, so that to read them is always already to interpret them. And his heroes are indefatigable interpreters, forced to practice a kind of doomed hermeneutics by a universe more ambiguous than any text. Joyce famously wished to write a novel that would keep the professors busy for a hundred years; yet the kind of annotation noisily demanded by “Finnegans Wake” looks childish next to the meditation quietly compelled by “The Trial” and “The Castle,” “The Hunger Artist,” and “The Penal Colony.”

At the same time, however, Kafka offers not the slightest hope that interpretation can be successful, or arrive at a complete and stable meaning. Josef K., in “The Trial,” never learns the charge on which he is convicted; K., in “The Castle,” never unravels the motives of the “gentlemen” of the Castle, who refuse to confirm his appointment as land surveyor. Yet in both novels, the problem is not the absence of clues, but their terrifying abundance. Every conversation and every gesture is potentially significant, so that the reader, like the two Ks, can scarcely avoid becoming paranoid. This is the universe’s revenge on hermeneutics. “In a light that is fierce and strong,” Kafka writes in one aphorism, “one can see the world dissolve. To weak eyes it becomes solid, to weaker eyes it shows fists, before still weaker eyes it feels ashamed and smites down him who dares to look at it.”

In “K.,” Mr. Calasso does not try to shed the kind of light that would solve the mystery of Kafka’s work, and thereby dissolve the work itself. He reproaches those readers who “seek rest in an all-encompassing interpretation” of Kafka by reducing him to just one of his many adumbrations – Freudianism or Judaism, surrealism or totalitarianism. Instead, Mr. Calasso – using the technique that he perfected in his admirable books on Greek and Hindu mythology, “The Marriage of Cadmus and Harmony” and “Ka” – leads the reader on a sort of dance through Kafka’s life and work. His short sections, which range from a few sentences to a few pages, pick up an episode, a phrase, a theme, and hold it up to the light of his quick intelligence, before setting it down and moving on. In this manner, Mr. Calasso deals with “The Castle” and “The Trial,” and more briefly with a number of the most famous stories – “The Hunter Gracchus,” “The Metamorphosis,” “The Burrow” – as well as Kafka’s letters and diaries.

Mr. Calasso is at his best in his surprising local insights and observations. Kafka is a strangely cinematic writer – one recent study, Hanns Zischler’s “Kafka Goes to the Movies,” was devoted solely to his moviegoing habits – but Mr. Calasso may be the first critic to point out that the scene in “The Castle” when K. becomes a school janitor is like “a Busby Berkeley musical,” “where the word gets stripped of its power and the gesture triumphs.” The Marx Brothers might be an even better point of reference, since Kafka’s comedy is often farcically subversive – as in the scene in which K. witnesses the distribution of Castle files, a solemn ritual that turns out to be elaborately, ludicrously careless.

Likewise, Mr. Calasso astutely points out that Block, Josef K.’s fellow defendant in “The Trial,” is Kafka’s harsh caricature of the assimilated Central European Jew, abjectly eager to please: “Whatever he does is the wrong thing, and yet it corresponds precisely to what is asked of him.” (It is an odd coincidence, unremarked by Mr. Calasso, that a similar Jewish figure in Proust is also named “Bloch.”)

But “K.” also pursues a larger argument. This has to do with what might be called Kafka’s metaphysics, and centers above all on “The Castle,” which often seems like “The Trial” reprised in the key of the supernatural. Drawing on the Hindu myths he wrote about in “Ka,” Mr. Calasso invokes the concepts of avyakta and vyakta, the “unmanifest” and the “manifest,” into which all of reality is divided. “The Castle,” he claims, takes place on “the dividing line between vyakta and avyakta,” which is also the boundary between the village, inhabited by human beings, and the Castle, inhabited by “gentlemen” who are clearly not quite human. Mr. Calasso elaborates Kafka’s sense that this otherworldly realm is both completely sealed away from our ordinary reality, and yet strangely vulnerable to it, so that the gentlemen must invent endless strategems to keep K. from breaching the Castle.

This is Mr. Calasso’s own rewriting of Kafka’s parable, as valid as that of any other good interpreter, but no more so, and certainly open to question. It is not clear, for instance, that Mr. Calasso’s Hindu terminology adds much to the more familiar words – earth and heaven, life and death – that we might use to name the realms that intersect in “The Castle.” Nor does Mr. Calasso sufficiently capture the pathos of Kafka’s sense that the other world, the world of the Castle and its angels or gods, actually wants to be violated. Rather than the Castle’s “hidden helplessness,” as Mr. Calasso puts it, we might speak of its secret longing, a longing that must be as powerful as the measures it takes to conceal that longing.

So, too, with Kafka, a writer who simultaneously yearns and refuses to be wholly understood. Perhaps the partial victory over Kafka’s mysteries that Mr. Calasso has won in “K.” is all that Kafka allows, or requires.