Monument for a miniaturist: a new museum dedicated to Paul Klee swells seductively into the Swiss landscape.

The arcaded streets of the old town of Berne, a UNESCO World Heritage Site, have acquired a counterpart in the pedestrian concourse that links the three volumes of the Zentrum Paul Klee, Renzo Piano's latest showcase for art. An undulating steel structure emerges from three hills to the east of the city, facing over the ringroad and surrounded by fields. It's a monument that celebrates the work of a brilliant miniaturist; a fusion of architecture and landscape, warmth and precision, structural daring and welcoming interiors. It captures the unique spirit of a native son who made his reputation in Germany, fled Nazi persecution to return home for a final burst of creativity, and is buried close by.

Klee was astonishingly prolific, meticulously recording the 10 000 works he created in his thirty-year career. 'Not a day without a sketch,' he noted in his journal, even as he neared his death in 1940. Members of the artist's family and the Klee Foundation promised to donate their astounding hoard of 4000 paintings and drawings if Berne would provide a dedicated space to show them. The chief sponsors were Professor Maurice Muller, a surgeon who invented the artificial hip, and his wife, Martha, who selected the location and the architect, and insisted that the building be a centre for all the arts and for people of all ages. Piano has created a museum that reaches out to embrace the visitors who stream in from footpaths, city bus, and motorway.

Like so many of his buildings, the Zentrum has a strong, simple diagram that belies the complexity of its design and construction. Piano shifted the site from the one that had first been chosen to address the sunken motorway, mirroring its gentle curve in the glass facade and even in the lines of vents cut into the floors of the galleries. That gives the building a symbolic link to the contemporary world, and to the city that lies beyond, concealed within its river valley. The undulating topography of the adjoining hills inspired the profile of the steel beams, which swoop and soar like a rollercoaster, rising from the earth at the rear to form a trio of imposing arches in front. Each rounded vault encloses a discrete set of spaces that are linked at the front by a 150m long glazed concourse containing the cafe, ticketing, shop, and reference area. Extended opening hours encourage visitors to come early or linger in this protected piazza. A changing selection from the permanent collection is displayed in the central pavilion, with a temporary exhibition gallery below. To the north, meeting and restoration areas lead out of the concourse, with a creative workshop for children below, and a subterranean auditorium behind. The south pavilion contains the administrative offices, archives, and seminar rooms, all on the main level.

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The 4.2km of steel girders were cut and shaped by computer-controlled machines but then, because each section has a different configuration, the 40km of seams were hand-welded. The arches are slightly inclined at different angles, braced by compression struts, and tied to the roof plate and floor slabs. In contrast to this assembly of unique parts, the concrete floors were constructed as a single structure, without settlement joints. The glass facade is divided into upper and lower sections, which are joined at the 4m roof level of the concourse, and are suspended from girders to avert stress from thermal expansion in the steel roof. The glass is shaded by exterior mesh blinds that extend automatically in response to the intensity of the light, and the high level of insulation minimizes energy consumption.

All of these measures pay off in the galleries and archives, where temperature and humidity must be maintained at constant levels, even though they are seamlessly linked to the busy public concourse. The permanent collection is displayed beneath the curved vault in a 1700sqm room that is divided by suspended flats into a benign labyrinth of interconnecting spaces. Each white screen hovers a couple of centimetres above the oak floor as do the peripheral walls. To achieve the low lighting level required by these sensitive works, illumination is indirect and filtered. Spots cast their beams on the white-boarded ceiling vault, and this glow is diffused by suspended square scrims.

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It's easy to see in the open geometry of the plan a reference to some of Klee's compositions, and the skein of slender cables supporting walls, lights, and scrims evokes his spidery penmanship. Piano's greatest feat is to give these tiny, intense works the space they need to breathe. Such a concentration of invention could easily overwhelm the viewer; here, each work seems to float in its own white void, bathed in a cloud of soft light, achieving an emotional as well as a formal resonance. Works are grouped, not chronologically, but by affinity, so that you can explore the infinite variety of ways in which this master employed line, colour, figurative and abstract imagery; always enigmatic and never repetitive. Toplit stairs and a piston-operated lift that is a work of art in itself carry you down to a room of similar size that presently houses the 366 sketches Klee did in his last fertile year. Here, the works are arranged on a peripheral and inner wall that trace the rectangle defined by slender structural columns. Scattered around both galleries on oak plinths are 40 hand puppets that Klee made around 1920 to amuse his family. Fabricated from the commonplace materials and crudely painted, they have a compelling talismanic quality, revealing the inner child in the artist and in all who connect with his work.

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That spirit carries over into the children's museum, aptly named Creaviva for its emphasis on creative play in a succession of workshops that are open to all ages. The steeply-raked 300-seat auditorium that burrows into the ground behind is a black box lined with curved sound baffles in the same orange hue as the Venetian plaster walls of the outer lobby. Regular performances of chamber music (Klee was an accomplished violinist), dance, and theatre will be interspersed with lectures and readings. All will reflect the versatility of the artist and his friends over four turbulent decades and their enduring legacy.

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