For lovers of The Girl with the Dragon Tattoo trilogy, a fourth book has been published.

The Girl in the Spider’s Web’ by David Lagercrantz

By LEE CHILD  SEPT. 1, 2015

There are many ways to continue a series after its author’s death. One is to wait a long time, until the original material has achieved classic status, and then find an established heavyweight willing to step up, like a great actor taking on his third King Lear. Examples would be John Banville reviving Raymond Chandler’s Philip Marlowe, or Jill Paton Walsh giving us more of Dorothy L. Sayers’s Lord Peter Wimsey. As readers we approach such attempts cautiously, with style points and degrees of difficulty in mind, as if we were judges at an Olympic diving competition, and therefore, however good the execution may be, these books will always remain to some extent interesting curiosities.

Another way is to continue as soon as possible, to give the newly bereft reader the sheer joy of another story with much loved characters and familiar scenarios. There are many such examples, but the all-time champ could be Robert Ludlum, who seems to have published nearly two dozen books in his lifetime, and considerably more than that after its untimely conclusion.

Some endeavors have a foot in both camps. ­Sophie Hannah’s Hercule Poirot is both a technical challenge and catnip to those craving more from Agatha Christie’s enigmatic Belgian. And now joining her is David Lagercrantz, with “The Girl in the Spider’s Web,” which continues Stieg Larsson’s Millennium series. That sequence was only three books long (“The Girl With the Dragon Tattoo,”  “The Girl Who Played With Fire” and “The Girl Who Kicked the Hornet’s Nest”) and, unusually, Larsson was dead even before the first installment came out. That sad and poignant fact launched the series from the features pages, rather than the book ­pages alone, which helped from a coldblooded promotional point of view. But there’s no doubt that its spectacular ­success was driven by its two central characters, the journalist Mikael Blomkvist and the — what, exactly? — Lisbeth Salander. Certainly, when the continuation was announced, there was joy on fan sites at the prospect of more from both of them — and in particular more from Salander, irresistibly tough, punkish, leather-clad, pierced and inked (including the dragon on her back) and at times unhinged.

Thus Lagercrantz’s first responsibility was to give us more of those two, which promised to be easy enough in Blomkvist’s case. Blomkvist is a journalist ­writing for Millennium, a Stockholm magazine dedicated to investigative reporting. In real life, Larsson was a journalist and so is Lagercrantz (as well as being a fine novelist in his own right), so we can expect him to know the terrain — although Larsson’s surviving long-term partner, Eva Gabrielsson, shut out of ownership or control by Sweden’s surprisingly behind-the-times attitude to inheritance by ­common-law spouses, feels that Lagercrantz lacks Larsson’s, and hence Blomkvist’s, passion and radical instincts. Which hints at ­Lagercrantz’s technical challenge. To what extent are fictional characters genuinely reproducible? To what extent are they animated by the singular psyche of the original author? To what extent can that author’s sparking synapses be detected through his language and served up again by another through his own?

Those challenges are only heightened by a character like Salander. She sprang off the page fully formed and vivid from her first appearance, as if shouldering aside the words to hover in the air between the reader and the book. It’s no exaggeration to say that as an invention she’s in the same ballpark as Thomas Harris’s Hannibal Lecter. She’s a classic antihero — fundamentally deranged, objectively appalling, lawless, violent and deceitful, but fiercely loved by millions of readers because she has good reasons for the way she is and a heart of gold. Can she be brought back to life by a different author — or will she lie inert on the slab? I opened the book, considering style points but mostly hungry for, yes, more of Salander.

Any Swedish crime writer’s first task is to decide whether to dodge or embrace the titanic shadow cast by Per Wahloo and Maj Sjowall, who 50 years ago began the 10-book Martin Beck series, which invented modern Scandinavian crime fiction and still stands as its finest achievement. Lagercrantz chooses to embrace that tradition, and thus the narrative feels calm, patient and familiar. An agnostic Jewish cop named Bublanski says sadly of his department, “Inevitably there were corrupt and depraved people in the force.” Both the line and the character could have been written by Wahloo and Sjowall. Other ­minor characters are introduced with full biographies and backgrounds, which isn’t a pacing error but rather a courteous, very Swedish, approach to storytelling.

The plot itself starts with computer hacking — into the National Security Agency in Maryland, no less — and Lagercrantz distinguishes himself by ­making the computer stuff very human. The technology serves the characters, rather than being a character itself. There’s a mute and autistic boy who needs protection and has vital clues locked in his head, which might or might not be revealed in a drawing. Lagercrantz distinguishes himself there too, with a fine and sympathetic portrayal. There’s artificial ­intelligence and code breaking and bad guys as icy and brutal as you’d like, but none of it is “techno” — its Swedishness, even as rendered in George Goulding’s English translation, keeps it very real and modest, a little romantic and a little inhibited. It’s a fine plot, with perhaps just one missed opportunity: American thriller writers know that if the N.S.A. were hacked, the response would be ballistic, hence offering a nice contrast between D.C. hysteria and Stockholm stoicism. But Lagercrantz makes nothing of it.

And what of Lisbeth Salander? Given that Lagercrantz knows she’s what ­readers want, her long and suspenseful introduction is masterful. It’s a striptease. She’s mentioned in the prologue (“One Year Earlier”), and then she’s not in the story at all, and then she is, maybe, purely by inference, and then we get a brief glimpse of her, and then another, and then some longer scenes. But it’s not until Page 216 that she actually speaks to Blomkvist. “Lisbeth,” he asks, answering her phone call, “is that you?”  “Shut up and listen,” she replies, and he does. And we’re off to the races. Or are we? Does she spark to life and get up off the slab?

Very, very nearly. After he reunites her with Blomkvist, Lagercrantz seems to lose his nerve. He relies too much on third-­party description — we’re told that Salander is intense and fierce, which is a poor substitute for seeing intensity and ferocity for ourselves. Certainly she’s appropriately brave, headstrong, smart and willful. And certainly the book’s stronger foot is firmly in the “sheer joy of a new story” camp. But the sublime madness of Larsson’s original isn’t quite there. Interestingly, Lagercrantz has a character pick up a copy of Stephen King’s “Pet ­Sematary” as potential bedtime reading. The conceit of that book is the existence of a patch of earth where, once buried, a dead pet or person will come alive again — but, crucially, diminished to a degree that depends on the time between death and the start of the magic process. It’s been eight years since the Swedish publication of “The Girl Who Kicked the Hornet’s Nest.” Was that too long? Was the hat-tip to “Pet Sematary” a coded acknowledgment that the task was impossible?

THE GIRL IN THE SPIDER’S WEB

By David Lagercrantz

Translated by George Goulding

403 pp. Alfred A. Knopf. $27.95.