INFERNO. By Dan Brown. 463 pages. Doubleday. $29.95.

One of the first characters to appear in “Inferno” is a spike-haired, malevolent biker chick dressed in black leather. She looks like trouble in more ways than one. What is the Girl With the Dragon Tattoo doing in Dan Brown’s new book?

She’s scaring Robert Langdon, the tweedy symbologist who stars in Brown’s breakneck, brain-teasing capers. Reader, she will scare you, too. The early sections of “Inferno” come so close to self-parody that Brown seems to have lost his bearings — as has Langdon, who begins the book in a hospital bed with a case of amnesia that dulls his showy wits. When Langdon of “The Da Vinci Code” can’t tell what day of the week it is, the whole Dan Brown brainiac franchise appears to be in trouble.

But “Inferno” is jampacked with tricks. And that shaky opening turns out to be one of them. To the great relief of anyone who enjoys him, Brown winds up not only laying a breadcrumb trail of clues about Dante (this is “Inferno,” after all), but also playing games with time, gender, identity, famous tourist attractions and futuristic medicine. Then there’s the bit with the symmetrical clockwise Archimedean spiral on Page 255.

There is even a twist built into its 14/5/13 publication date, a numerical anagram of 3.1415, the approximate value of pi. Why? Because Dante divided hell into circles. Because pi is a hint about measuring them. And because Brown’s readership has never met an embedded secret it didn’t like.

As is his wont, Brown begins with a crazily grandiose prologue, this one a little more unhinged than usual. “O, willful ignorants!” exclaims some mystery figure. “Do you not see the future? Do you not grasp the splendor of my creation?” That said, this guy with a God complex leaps off a building — or, as “Inferno” puts it, takes his “final step, into the abyss.” And then Langdon’s beautiful, ponytailed doctor yanks him out of bed so they can begin racing breathlessly through ... where?

Langdon thought he was in Cambridge, Mass., teaching at Harvard. But instead, he is in Florence, Italy, with his beloved Mickey Mouse watch gone (sigh) and his tweed jacket (bearing “Harris Tweed’s iconic orb adorned with 13 buttonlike jewels and topped by a Maltese cross”) in tatters. Sienna, the ponytailed doctor, happens to have an IQ of 208 and a neighbor whose locally tailored suit and loafers fit Langdon perfectly. So he’s looking very debonair as he dashes through the most famed and historically important sights in Florence, trying to figure out what a cylinder hidden inside a titanium tube with a biometric seal and a biohazard symbol is telling him.

It’s a tiny projector that offers a scrambled version of a Botticelli image, “La Mappa dell’Inferno.” And that sends Langdon and Sienna off to the races, engaging in one of those book-length scavenger hunts that Brown creates so energetically. “Inferno” picks three of the world’s most strategically significant, antiquity-rich cities as its settings, and Langdon makes a splendid tour guide and art critic throughout.

The formula also calls for sinister cultism of some sort, and in this case the dark scheming involves overpopulation. One character, Zobrist, is a wealthy Malthusian with a powerful, secretive, high-tech army at his command (Brown says it is real, but he has given it “the Consortium” as a fake name) and a doomsday plot to implement. While talking about controlling the rapid growth in population with the head of the World Health Organization, Zobrist is told, “We’re at seven billion now, so it’s a little late for that.” His reply, a fine specimen of mustache-twirling villainy: “Is it?”

There’s a lot more in “Inferno” along these lines. And it all ties together. Dante’s nightmare vision becomes the book’s visual correlative for what its scientific calculations suggest. But the main emphasis here is on the prodigious research and love of trivia that inform Brown’s stories, the ease with which he sets them in motion, the nifty tricks and the cliffhangers.

Finally, there is the sense of play that saves Brown’s books from ponderousness, even when he is waxing wise about some ancient mystery or architectural wonder.

Once the globe-trotting begins in earnest, private planes figure in the story and Langdon calls his publisher to ask for one. No, says the publisher, then adds: “Let me rephrase that. We don’t have access to private jets for authors of tomes about religious history. If you want to write ‘Fifty Shades of Iconography,’ we can talk.”

Guess what: Brown already has written it. And then some.

Reviewer Janet Maslin writes for The New York Times.