Bjork isn't that weird. Granted, expectations are pretty high, what with the swan dress at the Oscars, and the video in which she turns into a polar bear, and the freaky electronica-based whisper-wailing music she makes, and the fact that she's from Iceland. But still, in person, she is very close to normal. Conversation is cohesive. References are erudite. Return questions are volleyed. Humility is invoked. Offers to taste her beverage are proffered. Eating is done with a knife and fork. It is, without a doubt, terribly disappointing.

The only thing that hints at the weirdness widely attributed to her is this: Bjork believes in elves. Fairies too. "We think nature is a lot stronger than man," she explains, sipping a cappuccino at Vid Fjorubordid, a restaurant on the ocean that is virtually the only commercial enterprise in Stokkseyri, Iceland, a town so small that the road entering it has a sign of geometric symbols with a line through them, meaning "no town here." The road also has a waterfall with a rainbow over it and graffiti mowed into the hills, so you can see where the elf thing came from. "My family hunts half the food we eat. A relationship with things spiritual hasn't gone away," Bjork says, in defense of elf-faith. "In a lot of Western cities, they lost that and had to buy it again with meditation courses." In fairness, despite the fact that Icelanders have a 99.9% literacy rate, most believe in elves. In fact, the government had to reroute a planned highway because it would have passed over elf territory. It appears that elves, while remaining hidden, somehow manage to hand out their maps.

At the Stokkseyri restaurant, Bjork, 35, is wearing a coat of cow fur, an embroidered one-sleeve dress with a wine stain on the chest, mukluks with red plastic horse fencing for laces and a blue, lunch-box-shaped pocketbook. The outfit, she explains, looked much more sensible the night before, when she and a friend were up until 4 a.m. in Reykjavik bars before driving an hour to the friend's summer home in Stokkseyri. They spent the night at small bars far more mellow than the popular club Thomsen, which she does not recommend. "It's kind of..." she says, using her index finger to point the top of her nose in the air. "Puff Daddy might be there."

So even if she's not that strange in person—allowing for ethnic background on the elf thing—there's no getting around the fact that Bjork's music, which has sold 10 million units worldwide, is really weird. Her latest album, Vespertine, uses household noises as instruments: the shuffling of cards serves as a beat on one song, as does clattering cutlery, icicles melting, footsteps in snow, clicking cameras, beating on a thermos and pounding on, yes, the kitchen sink.

This recording is Bjork's return to Iceland—or Scandinavia, at least—after a career of mixing cultures: posing as a Chinese woman in Asian dress on the cover of her last album, Homogenic, and collaborating in past projects with American rapper RZA and British musicians Goldie, Tricky and Thom Yorke. The album was written mostly while she was in Denmark (which controlled Iceland until the mid-20th century), shooting the 2000 film Dancer in the Dark and feeling homesick. "My album is sort of chamber music for this century," she says, scratching a mosquito bite on her arm. "After traveling so much, I realize how gorgeous the Internet is, bringing the home together again. So I'm looking back on a living room in the '50s where the whole family is, but it's modern and technological."

For the album's effects, she chose low-key noises that sound good when downloaded—acoustic instruments, a music box, a whispered voice. This also reflects tech-heavy Iceland, which has more cell phones and Internet connections per capita than any other country. If you lived on an island that is mostly flat, barren, rocky, frozen landscape, you would make sure you had an Internet connection too.

Bjork—when there are 280,000 people in your country and you use the patrilineal Viking system for last names (in her case, Gudmunsdottir), first names are enough—has come back from her new home in New York City to drop off her son Sindri, 15, who chose to go to high school in Reykjavik and live with his father Thor Jonsson, who used to play with Bjork in their '80s punk band, the Sugarcubes. She is sad that Sindri is leaving her for the first time, but she tries to act tough. "At that age, you need to be with your mates," she says. She likes the idea that her son will grow up Icelandic, but she is leaving a part of herself behind here.

Though she says she loves New York, cities still make her uncomfortable. "The first time I went to London, I'd walk for three or four hours and couldn't find a way out of the city. Only now have I begun to enjoy the strain of a city. Cities are bad for you, and I kind of like that. It compresses you and can be very stimulating." Not exactly what Rudy Giuliani would use for a motto, but an endorsement nonetheless.

Besides her apartment in the West Village neighborhood, she has a work space in Chelsea, a two-bedroom apartment where her assistant and an electronica dance duo named Matmos live. (Matmos' latest album, A Chance to Cut Is a Chance to Cure, contains sounds sampled during plastic surgery.) Down the street from the Chelsea apartment, the Matthew Marks gallery is showing Bjork's upcoming video, five minutes of multicolored, multitextured gloopy stuff running from her eyes into her nostrils and back out her eyes. Bjork maintains, paradoxically, that she has to create videos that odd to make her music more accessible. "If I do a song, people have to listen to it 10 times to grasp it; but if they have an image to go along with it, they only have to listen to it a couple of times," she says. Her commitment to art extends to putting together a new $35 coffee-table book, Bjork, consisting mostly of pictures of her. It took the publisher, Bloomsbury USA, a very long time to convince her that it couldn't make the book out of glass.

The artiness explains the swan dress she wore at the Oscars. Fashion has always helped her stand out—a priority for Icelanders, where mostly everyone is blond (kids called her China Girl in elementary school) and, as a recent genealogical study showed, people are a little closer to one another than they ought to be.

So like Iceland generally, the young Bjork was hungry for world music—the Beatles count as world music in Iceland—even though her background was classical. At one point in the Stokkseyri restaurant, she starts humming Tchaikovsky's Nutcracker Suite before she catches herself. Another time, back in Manhattan at the Wild Lily Tea Room, she notices not only that the restaurant is playing French composer Eric Satie but that the music is being played on a harmonium instead of a piano. "I was put in music school when I was five, where they taught German 18th and 19th century, which is called classical music, which I think is very funny. To be told that 200 years of German music is it, and the rest is crap—I wasn't buying that as an Icelandic person," she says, sticking her tongue halfway out.

A prodigy who reportedly sang before she talked, Bjork became an Icelandic pop star at 11. From there she formed a series of punk bands, including the internationally popular Sugarcubes. "I felt pretty strongly about being truthful about what it means being a girl in Iceland," she says. "The other way was just to play Icelandic music, and I don't think that's truthful either. Even in Iceland, you go to a taxi and you hear jazz, and you go to a restaurant and you hear Indian music."

To give her music a truer feel, Bjork went pretty far this summer. Taking off from Manhattan ("I don't like heat. I feel like I've done 10 Valiums"), she spent a month in an aluminum igloo in Ilulissat, Greenland, with her boyfriend, artist Matthew Barney. There she assembled a choir of Inuits and taught them her songs, line by line. That was a group far different from the uber-precise classical choir she hired last spring for two semisecret shows in New York's Riverside Church that she opened by walking down the aisle holding a candle and singing. At those she was backed not only by the chorus but also by a harpist and a full orchestra, plus Matmos. Now that whole production is on a U.S. tour, her first in three years. Though Bjork could pack larger houses, she handpicked smaller venues, mostly opera houses, because she felt her songs were too intimate for larger settings. "I'm not going to make money," she concedes. "I never consider that. Music comes first. Life's too short."

While Bjork's insistence that music come from within gives her collaborators creative leeway, it also makes her hard to read, say the Matmos guys. Instead of telling them to pump up the bass, she offers less direct suggestions. "'Primordial with no history,' that's the kind of instruction she gives us," says M.C. Schmidt of Matmos. "The other instruction was to 'make it like a garden,'" says band mate Drew Daniel. Other than that, the duo insist that Bjork has been exceedingly normal. Says Daniel: "She's a parent. She's 35. She's not doing the epater la bourgeoisie thing. What is unusual is that the filters and shame and self-editing that go with being an adult seem optional to her."

And she keeps her cool. At a party after one of the Riverside Church concerts, says Daniel, a man started throwing glasses at the bartender, with shards flying everywhere. One of the choir members ran over to Bjork, saying, "We have to protect your face." Bjork laughed and said, "Protect my drink." Bjork even acted as a DJ at Daniel's 30th-birthday party, taking the task very seriously. This simultaneously flattered and worried him. "She's got terrible taste in pop music," he said beforehand. "I'm afraid she's going to play Foreigner." She didn't.