Urban flight.

Zaha Hadid wants to make buildings fly. Seemingly obsessed with images of lightness, with fantasies of buildings frozen as they explode into fragments, she has long fought the laws of gravity. Gravity has won. Now Hadid's "deconstructivist" architecture an expressionistic blend of fragmented forms inspired by Soviet Constructivism and vague notions of disorder has a center that holds. And this London-based architect's work has undergone a delicate transformation: from abstracted drawings of buildings that float and slip across the paper to concrete projects more deeply anchored in the realm of building.

Hadid's current show in the capacious waiting room of Manhattan's Grand Central Terminal - a show still in the planning at this writing - highlights this transformation. Moving along past the walls of the Beaux Arts hall, visitors will see only recent projects: photos of the completed Vitra fire station in Well am Rhein alongside formal drawings of the Cardiff Bay Opera in Wales - a project now awaiting final approval. Not included in the show is Hadid's new proposal for Manhattan: she is awaiting the results of a competition at the other end of 42nd Street - a plan for two hotel towers that will anchor the street's "entertainment corridor."

Hadid was born in 1950 into the cultural elite of Baghdad, where her industrialist father once led Iraq's democratic opposition. The young Hadid was educated in Swiss and English schools. In 1968, she returned to the Arab world, where she studied mathematics at the American University in Beirut, at the time a city embroiled in social tensions: "It was staring you in the face - miles of camps of Palestinians and Kurds," she recalls. Hadid existed on the border between sometimes incompatible traditions, and she was drawn to their contradictions. In some sense, the idea of culture as something in constant flux must have had a distinct attraction. "Being displaced was a very liberating experience," she says.

In 1972, Hadid returned to London to attend the Architectural Association, the only truly internationalist architecture school of the time, and one swarming with dissonant architectural factions. She eventually studied with the Dutch architect Rem Koolhaas, who was researching the modern metropolis. Koolhaas' dialogue was with the 20th-century masters of architecture, not with the distant past. It was the first time Hadid was exposed to an explicitly Modernist agenda.

It was in Koolhaas' work that Hadid's sensibility found its closest kinship. Their mantra was an unrestrained admiration for the congestion, dynamism, and even brutality of the city. Neither rejected the Modernist experiment outright. Instead, they were looking for ways to include in their architecture the parts of the city that the Modernists forgot: places of friction and contradiction. The more ardent and rigid Modernists - like the Soviet Moisei Ginsberg - were rejected in favor of those who were more formally complex. "We felt basically there is no functionalism," says Koolhaas. "So we should deal with these conditions that are architectonic rather than functional."

Koolhaas recalls that his goal was "developing this parallel between the architecture of Manhattan and the architecture of the Soviets. We were dismantling one of [Kasimir] Malevich's tektonics and working on each part as an autonomous program, and then re-assembling it again" as a piece of Manhattan architecture. Malevich was an apt choice: his "tektoniks" depict tight groupings of abstract bars of shifting sizes, and he was distinctly antiutilitarian. Koolhaas' idea was to re-create the spontaneity of the city, where random functions are compressed into odd spaces, and unexpectedly juxtaposed one against the other.

At the time, architecture's emerging avant-garde - Koolhaas, Bernard Tschumi, Peter Eisenman - were all busily writing theoretical tracts about the metropolis. Koolhaas, for instance, was completing Delirious New York. But Hadid's role models were not theorists. She chose an aggressive celebration of Modernism's heroic elements. Like Gothic pinnacles turned on their sides, her imaginary cathedrals soared across the landscape. Hadid was inspired by Malevich's "tektonics" because his forms existed in a weightless world. As such, they seemed freed from existing order. Hadid's mission was to make architecture soar.

It was "The Peak" - Hadid's entry in a 1982-83 competition for a men's club that jutted off the edge of a cliff above Hong Kong - that defined her new architectural language. A cluster of inhabited "beams" were to plunge like Zeus' thunderbolts into the side of a mountain. The building was bisected by a path that led to a viewing deck. "The site was inappropriate for a little club," she says, "my idea was that people should move right through it."

Hadid won the competition, but the project fell through, and rumors began to circulate that her architecture was unbuildable. Some also saw the language of "deconstructivism" - which seemed in architecture to mean above all else the fragmentation of space - as nihilistic, its sharp angles and knifelike concrete edges as inhuman. Worse, these splintered fragments risked slipping into hollow metaphors for the notion that order has no center. Though the Peak would actually have been engineered like any banal elevated highway, on paper it seemed to explode chaotically across the page.

"People have not observed the work develop over the past five years," says Hadid with slight exasperation. "It was never really about deconstruction. What changed dramatically was the move from the plan to the volume - to making spaces. It really occured with Kurfurstendamm 70 [a narrow office building Hadid designed for Berlin in 1986], because the space was so tight, it really required tremendous precision in the placement of the elements."

Kurfurstendamm 70 and a riverfront art-and-media center designed in Dusseldorf in 1989 (both unbuilt) marked a key shift in Hadid's work. The cliches of flight were now anchored with surprising heaviness. At Dusseldorf, in fact, they were abandoned altogether. Rather than unraveling over the site, the project was compressed into a glass wall of studios and offices. The complexity of the program animated the design. A large triangular plane was to pierce through the middle, visually connecting the street to the water's edge. At one end, vertical slabs would break away from the wall to form separate departments and conference halls. Such newly compressed forms were more in keeping with Hadid's professed goal of reversing the disintegration of the late-20th-century city into a sprawling megalopolis.

At Weil am Rhein - Hadid's first significant built structure - this transformation was even more apparent, but the change went largely unnoticed. Critics attacked the building for its "narcissism" and "unruliness." Actually the Vitra factory's fire station is bunkerlike and compact. The changing room and exercise area is encased in two elongated concrete forms that sit heavily on the ground, one breaking through the wall of the other and forming the stair and entranceway. Above, two triangular concrete slabs float lightly, tilted upward and breaking away from the building. The tension between the two - the image of flight locked into the weight of gravity - gives the work a complexity that was new in Hadid's work.

More important, Vitra seems to draw in the geometry of the site rather than break it apart. Hadid stages what she calls "a dynamic pattern to allow the spaces to gradually develop." It is an echo of the Portugese architect Alvaro Siza's words that architects only "transform reality." But Siza manipulated the forms of his buildings to respond visually to what was around them. Hadid's flourishes remain more expressionist and sculptural.

In her more recent Cardiff project Hadid expresses the struggle between private and public, isolation and contact, more aggressively. The opera house is both centered like a medieval fortress and rooted in the frantic movement of the city. The theater looms at its center, the service building curled around it like a defensive wall, their proximity heightening the visual tension between them and the sense of an internal world. But these internal spaces are pierced and pried open. The surrounding service building is lifted up to make room for a foyer below, while its roof becomes an open-air plaza. Both these public spaces connect directly to the street. Above, more decks sprout from the theater. "We wanted to make a large public room that could work as an outdoor room and an indoor room," explains Hadid. Like Constructivist "social condensers," these spaces are meant to encourage contact.

Cardiff seemed the perfect context to create the model of a new vision: a bleak port town trying to reclaim the glory days when it was busy exporting coal from the neighboring mines; a stagnant bay that has festered and rotted since the advent of oil destroyed the city's economy; and a neighborhood of banal, haunting office parks designed during the '50s. But when the opera-house design was unveiled last September, it caused a hysterical brouhaha. London critics pitted themselves almost weekly against local developers, who claimed to be looking for a clearer national symbol to dispel Cardiff's barren image. Others felt that in a country where women make up a paltry 8 percent of the architectural profession, this resistance is misogynist and perhaps racist. "It is not overt but you can feel it," admits Hadid, "I don't know which - if it is misogyny or racism. But I ignore it."

Hadid's New York Show - the first ever for an architect at Grand Central - will feature drawings of the Vitra, Dusseldorf, and Cardiff designs. Limited funds scuttled the original plan to build a flying beam that would bridge the room. Instead, a simpler "room within a room" floats six inches off the ground, one end opening up like a gaping mouth. Inside, images of Vitra and Dusseldorf line the walls, and Hadid plans to carpet the floor with a map of a new project, the Spittelau housing development in Vienna.

At its best, Hadid's show echoes an urbanism lodged deep in New York's cultural memory. While the trend among developers here is to suffocate the immense public hails around us with restaurants and shops, projects like Dusseldorf and Cardiff at least seem to acknowledge the often forgotten tradition of cities as great social spaces. These projects embrace the city as antisuburb: a place whose congestion is necessary for social and cultural interaction, not necessarily frenzied consumption. Hadid's "kind of building is Grand Central - a building that extends the city inside. Subways, trains, roads, mixed sociologies - her buildings are always urbanized," says critic Joseph Giovannini, a longtime champion of her work.

Hadid will try to engage this energy more directly in Times Square. She is proposing two hotels - one a 50-story upscale palace, the other more down-scale and half the height - that at least visually will bridge the street. And although she is bound by contract not to discuss the competition, her interest clearly lies in the expansion of public space: the New York lobby's traditional openness to the street, the city's web of underground passageways, the funneling of 6,700 buses a day in and out of Port Authority. "We went into all the subway areas - really gruesome and stifling," says Hadid, "But one can imagine a world like Rockefeller Center, where you can multiply the activity. One can begin to infiltrate all these territories." Whatever her solution turns out to be, the strategy is right.

Delmore Schwartz once described a metropolis "full of traffic, accident, commerce and adultery... Its belly veined with black subways, its towers and bridges grand, numb and without meaning." This is the city Hadid would awaken. While developers gleefully sweep away the Times Square area's Bladerunner-like chaos of sex shops, abandoned theaters, and artist's workspaces, Hadid's models allow for the space of spontaneity, and at moments suggest ways to lift the weight of the city from our backs while letting it ramble on.

Zaha Hadid's Grand Central Terminal exhibition remains open into February; at this writing, its closing date is undecided.