Cottbus kaleidoscope: this library enlivens both the campus and civic realm of a former industrial centre striving to reinvent itself.

Cottbus, a banal industrial city near the Polish border, is worth a fast hour's drive on the autobahn from Berlin for its quirky Jugendstil theatre, and as an incentive to continue on to Wroclaw (the former Breslau), a repository of classic modern buildings. Head south, and you can stay overnight at Lobau in Hans Scharoun's 1933 Haus Schminke. Herzog & de Meuron's new university library deserves its place in this pantheon, as an example of how the Swiss partnership fuse rigorous analysis with poetic beauty.

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Located near the main entrance to Brandenburg Technical University, an institution founded in 1991 to help reinvigorate the decrepit shell of this workers' paradise, the new library serves as a bridge between town and gown. It is also a symbol of transparency and free expression, in a way that the uniform campus buildings are not. By day, it shimmers on a grassy knoll (a former sports field) just off Karl-Marx Strasse, the undulating folds of screen-printed glass reflecting every passing cloud; at night, it's a beacon. The organic form narrows and swells as you move around it, and the curved bays flow into the landscape, creating a strong sense of place. It also has scale and substance, in contrast to the same architects' Allianz Stadium in Munich (AR June 2005) which resembles a huge balloon that might deflate if punctured by some hooligan.

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As Herzog & de Meuron demonstrated in the recent exhibition of their work at the Schaulager in Basel and later at the Tate Modern (AR July 2005), every project begins with study models, and a consideration of materials. The library plan morphed from a circular disc of acrylic into a series of amoeba-like shapes that were determined, as the architects insist, by 'a purposeful configuration of many different flows of movement ... and their ability to reorganise and restructure urban space'. The shape generates a sensuous presence in a relentlessly orthogonal frame, while maximising the exposure of the interior to natural light and views.

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That spirit of joy and exuberance is sustained throughout the seven-storey building. In contrast to most libraries, in which reading areas are ranged around a core of books and stacked repetitively on top of one another, here the floors are cut away to provide a diversity of spaces, each with a distinct character, and each a part of a single interior volume. Some reading areas are two or three stories high and are bathed in natural light from the sides and above, while others have intentionally low ceilings to provide intimacy and enclosure.

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A sober palette of white and grey fosters concentration, but the circulation areas at the centre are an explosion of colour. Floors are painted in ultra vibrant stripes that are reflected in the metal ceilings and shelves. These coruscating hues are picked up in the cylindrical lift, and a 6m-diameter spiral stair that drills through the building like a giant corkscrew. When viewed from below it becomes a pink and green hallucinogenic vortex, but is also, more prosaically, a vertical street on which students and staff can linger to chat.

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Patterned skins are a Herzog & de Meuron signature, and there's a fascinating contrast between the figurative facades of etched glass and concrete in their library at Eberswalde, an hour north of Berlin, and the abstraction of Cottbus. Its glazed shell is printed on both sides with words in different tongues and alphabets, superimposed to become a meta language. The two layers of silk-screened dots achieve a moire effect that softens the expanses of glass, blocks glare, and screens out distractions. Nighttime illumination is provided by corkscrew chandeliers supporting corkscrew bulbs which transforms the building into a glowing organism, enticing the studious into its depths.