Stedelijk Museum Amsterdam

Stand for a moment on the open grass of Museumplein and listen. Bicycle bells, the scuff of shoes on gravel, a tram humming somewhere behind you. Ahead, two buildings sit side by side, and they could hardly be more different. On one side is warm red brick, with stone trim and tall windows. On the other is a vast white form, smooth and seamless, that seems to float above glass. This is the Stedelijk Museum, Amsterdam's home for modern and contemporary art and design.

The name itself is a small clue. In Dutch, "stedelijk" simply means "municipal", or "of the city". So this is, quite literally, the city museum. It did not begin as a temple of the avant-garde. It began in the late nineteenth century, partly thanks to a bequest from a wealthy collector, Sophia Augusta de Bruyn-Lopez Suasso. Her collection was full of decorative objects, jewellery and curiosities. The building was made to hold them, and the city's own collections too.

Look first at the older building, the brick one. It opened in 1895, designed by the city architect Adriaan Willem Weissman. Its style is often called neo-Renaissance — a nineteenth-century revival of the grand buildings of sixteenth-century Europe. Notice the gables, the pale stone bands that run across the red brick, and the niches along the facade. It feels solid, civic and a little formal. It was built to say that Amsterdam took culture seriously.

Now turn to the white wing. Most visitors arrive here today, because the main entrance moved to this side. The extension was designed by the Dutch firm Benthem Crouwel Architects and opened in 2012, after years of renovation. Locals quickly gave it a nickname — "the bathtub". Once you hear it, it is hard to unsee. The curved white shell really does look like an enormous bath, resting on a wall of glass.

Here is the first surprise. That white surface is not stone, and it is not painted concrete. It is a composite material, reinforced with strong synthetic fibres, the same family of fibres used in demanding industrial products. This allowed the architects to make a huge, smooth shape with no visible joints. Run your eyes along it and try to find a seam. The idea was to make the new wing feel light, almost like an object placed on the square.

The design was controversial when it opened. Some people loved the bold contrast with the old brick. Others felt it was too playful next to a historic facade. That argument is part of the story, because this museum has always lived on the edge of what the public is ready to accept. A building for new art, the architects reasoned, should not hide behind old forms. Whether you agree is entirely up to you.

The person who did most to shape the museum's character was Willem Sandberg, who became director after the Second World War. During the war, Sandberg was active in the Dutch resistance. He took part in an attack on Amsterdam's population registry, an attempt to destroy records the occupiers used to track people. He had to go into hiding. When peace came, he brought that same courage to the museum, and he turned it towards the art of his own time.

Sandberg was also a graphic designer, and this is the second surprise. He designed many of the museum's posters and catalogues himself, often with torn paper shapes, bold colour and simple type. Under his leadership, the Stedelijk became known as one of the liveliest museums of modern art anywhere. He showed young, difficult artists alongside established names. Design, posters, furniture and photography were treated as seriously as painting. That mix still defines the collection today.

Inside, you will meet some of the great movements of the twentieth century. The museum holds an important group of works by Kazimir Malevich, the Russian painter who pushed art towards pure geometric shapes. There is also strong work from De Stijl, the Dutch movement of straight lines and primary colours, including paintings by Piet Mondrian. Look out for the Red Blue Chair by Gerrit Rietveld — a chair that is almost a diagram, built of flat boards and painted planes.

The collection also tells a very Amsterdam story through CoBrA. This was a group of artists from Copenhagen, Brussels and Amsterdam — the name comes from those three cities. After the war, they rejected polished technique and painted with the raw energy of children's drawings and folk art. Karel Appel is the best-known Dutch member. When the museum first showed their work, many visitors were shocked. Today, those thick, bright, wild paintings feel like an essential part of the city's character.

One of the most loved works here is by Henri Matisse — The Parakeet and the Mermaid. Late in life, when illness made painting difficult, Matisse cut shapes from paper painted with colour and arranged them on the wall. The result is large, joyful and full of leaves, fruit and swimming figures. Stand back from it, then step closer. You can see the slightly uneven edges where the scissors moved. The hand of the artist is still there.

Not every story here is gentle. In 1986, a visitor attacked Barnett Newman's large painting Who's Afraid of Red, Yellow and Blue III, slashing the canvas. The restoration that followed became a public debate of its own, about how a damaged artwork should be repaired. It is a reminder that modern art can stir strong feelings. Collections change and works rotate, so not everything mentioned here will always be on view. Part of the pleasure is finding what is out today.

As you move between rooms, notice how the building guides you. The older galleries have tall ceilings, daylight and a classic rhythm of rooms. The new wing feels more open, with long sightlines and clean white walls. Walking from one to the other is like crossing from the nineteenth century into the twenty-first. The museum also keeps space for temporary exhibitions, so the newest art in the city often appears here first.

When you step back outside, pause on Museumplein before you go. The Van Gogh Museum stands close by, the Rijksmuseum closes the far end of the square, and the Concertgebouw concert hall sits behind you. Look once more at the brick and the white bathtub, side by side. One was built to show that a city cared about the past. The other was built to show that it still cares about what comes next.