Gropius took the job in a Germany that had just lost a war and acquired a republic, in a burst of liberalisation that made room for experiment the old order had suppressed. His name for the school pointed backwards as much as forwards: Bauhaus evokes both building and the Bauhütte, the premodern lodge of stonemasons. In an April 1919 exhibition pamphlet he set out the goal as creating "a new guild of craftsmen, without the class distinctions which raise an arrogant barrier between craftsman and artist." The first faculty was small - Johannes Itten, Lyonel Feininger, the sculptor Gerhard Marcks - and grew quickly to include Oskar Schlemmer on theatre, Paul Klee, and from 1922 Wassily Kandinsky. Itten shaped the school's pedagogy from 1919 to 1922 through the Vorkurs, the preliminary course in materials, colour and form that every student took and that art schools worldwide would copy.

The Bauhaus declared equality between the sexes and accepted women from the start, and in its first year more women applied than men. Gropius's response was not what the manifesto implied. He announced that for the foreseeable future only women of extraordinary talent would be admitted, and the surplus were given a workshop of their own - which became the weaving workshop. Women who arrived intending to build, paint or sculpt found themselves at looms. Some of them made the looms into a triumph anyway. Gunta Stölzl returned to lead the weaving workshop in 1926, becoming the first woman to head a department and the only woman ever to hold the rank of master at the school. Marianne Brandt got into the metal workshop and succeeded László Moholy-Nagy as its studio director in 1928, designing lamps and metal vessels that remain among the school's most recognisable objects. Anni Albers arrived in 1922 and made textile design a serious modern discipline. Lucia Moholy photographed the buildings; the crisp black-and-white images through which almost everyone knows the Bauhaus are hers.

Thuringia's conservative politicians moved against the school as tensions rose after 1923, halving its funding and putting staff on six-month contracts; on 26 December 1924 the Bauhaus announced its own closure for the following March. It reopened in Dessau in 1925, with Gropius's new buildings inaugurated late in 1926. Then came the arguments. Gropius resigned in February 1928 and was succeeded by Hannes Meyer, who swung the focus from aesthetics to function - five balcony-access apartment blocks for Dessau that are still lived in, and the ADGB Trade Union School at Bernau bei Berlin. Meyer also gave one day a week to sport and gymnastics, on the grounds that design suffered from too much brainwork. Ludwig Mies van der Rohe replaced him in 1930, interviewed every student individually, dismissed the ones he judged uncommitted, stopped the school manufacturing goods at all, and hired no new faculty except his collaborator Lilly Reich.

When the Nazi Party took control of the Dessau city council in 1931, it moved to close the school. In late 1932 Mies rented a derelict factory on Birkbusch Street in Berlin with his own money; students and faculty rehabilitated the building themselves and painted the interior white. It ran for ten months. In 1933 the Gestapo shut it. Mies argued his way to the head of the Gestapo and secured a letter permitting it to reopen, and then he and the faculty closed it voluntarily anyway. The dispersal that followed is usually told as a triumph, and for the emigrants it largely was. The rest of the record is harder. Of the students enrolled when Hitler came to power, roughly 900 are thought to have stayed in Germany; of those, 188 joined the National Socialist Party, twelve joined the SS, and one worked on the design of the crematoria at Auschwitz. A school does not determine what its graduates become.

Gropius, Marcel Breuer and Moholy-Nagy regrouped in London, in the Isokon flats on Lawn Road. Gropius and Breuer went on to the Harvard Graduate School of Design, where their students included Philip Johnson, I. M. Pei and Paul Rudolph. Mies settled in Chicago to run the architecture school at what is now the Illinois Institute of Technology, and Moholy-Nagy founded a New Bauhaus in the same city. German-Jewish architects fleeing the regime built more than 4,000 International Style buildings in Tel Aviv, whose White City UNESCO listed in 2003. Later critics were less reverent, complaining of a utopia built on a mechanical view of human nature - "home hygiene without home atmosphere." And the single most profitable product the school ever sold, after all its radical theorising about form and function, was wallpaper.