Thyssen-Bornemisza Museum

Step in from the Paseo del Prado, and the noise of the traffic falls away almost at once. The air is cool. The floors are smooth and pale under your feet. And then there is the colour of the walls... a warm, dusty pink, somewhere between salmon and terracotta. It is not the white box of a modern gallery. It feels more like a private house, which is exactly what this place once was.

You are standing inside the Thyssen-Bornemisza Museum, one corner of what Madrid calls its Golden Triangle of Art. The Prado sits just across the boulevard. The Reina Sofía, home of Picasso's Guernica, is a short walk south. Many visitors treat this museum as the middle stop between the two giants. But it does something neither of them does. It tells the whole story of Western painting, from the late Middle Ages to Pop Art, in one continuous walk.

The building itself is the Palacio de Villahermosa, a neoclassical palace from around the turn of the nineteenth century. Neoclassical simply means it borrows the calm, ordered lines of ancient Greece and Rome. From outside, it looks restrained, almost modest, beside the grand Prado. Inside, the Spanish architect Rafael Moneo reshaped the rooms for the museum's opening in 1992. He gave the galleries skylights, so that daylight falls softly from above onto the paintings.

Now, the surprise. This collection was not built by a nation, a king, or the Church. It was gathered by one family, across two generations. Baron Heinrich Thyssen-Bornemisza, from a German and Hungarian industrial dynasty, began buying Old Masters in the early twentieth century. His son, Baron Hans Heinrich, kept going, and pushed the collection forward into modern art. For decades, much of it hung in the family's villa in Lugano, in Switzerland.

So how did a Swiss-based private collection end up in Madrid? Part of the answer is a woman named Carmen Cervera. She was a former Miss Spain, and she became the baron's wife. Many people credit her with steering the collection toward her home country. Several countries wanted it. Spain first borrowed the paintings, and in 1993 the Spanish state bought the core collection. It was one of the great art acquisitions of the late twentieth century.

Here is the best way to walk it. Take the lift or the stairs to the top floor, and begin there. The museum is arranged roughly in time order, and it runs downward. On the top floor you meet the early Italian and Flemish painters, with gold backgrounds and serious saints. As you descend, the centuries move with you. By the ground floor, you have arrived in the twentieth century.

On the upper floor, look for a young woman in profile, painted by the Florentine artist Domenico Ghirlandaio. She is Giovanna Tornabuoni, and she sits perfectly still, in a rich gown, against a dark niche. Behind her, a small Latin inscription and a little shelf of objects give clues to her life. Many people consider her one of the most beautiful portraits of the Italian Renaissance. Stand close. The detail of her necklace rewards the effort.

Nearby, you may find a full-length young knight in armour, standing in a landscape full of plants and animals. This is by Vittore Carpaccio, a Venetian painter. It is one of the earliest full-length portraits in European painting. Take a minute with the background. Small creatures hide in the grass and water, and each plant is painted with a naturalist's care. Most visitors look only at the knight, and miss the little world around him.

A few rooms on, there is a small panel of King Henry the Eighth of England by Hans Holbein the Younger. It is surprisingly small. You may expect the king to fill a wall, but here he fits in a frame you could almost hold. Yet the painting carries real power. The heavy face, the jewels, the direct gaze... this is the image of Henry that most of us carry in our heads.

As you move down through the floors, the light in the paintings changes. Caravaggio's dramatic shadows give way to Dutch interiors, then to the open air of the Impressionists. Here is the second surprise. This museum holds one of the strongest groups of nineteenth century American painting anywhere outside the United States. Wide landscapes of rivers and mountains, by painters most Europeans never studied. It is a rare chance to see them on this side of the Atlantic.

By the time you reach the twentieth century, the walls fill with names you will recognise. German Expressionists, with their sharp, loud colours. Cubist experiments by Picasso and Braque. A lonely woman in a hotel room by the American painter Edward Hopper, reading a letter in hard, quiet light. And a bright, comic-strip woman in a bath by Roy Lichtenstein. The jump from Ghirlandaio's calm profile to Lichtenstein's dots is the whole point of the walk.

There is also a newer wing, opened in the early 2000s, which holds paintings from Carmen Cervera's own collection. Her taste leans toward landscapes, Impressionism, and Spanish and Catalan painters. The museum also runs temporary exhibitions, often in its basement galleries. If you have energy left, check what is on. And if you need a break, there is a café and a garden terrace, where you can rest your feet before the next stretch.

Before you leave, pause in the entrance hall, or step back out onto the Paseo del Prado. Look across at the plane trees, the fountains, and the stream of cars and cyclists. In a single afternoon, you have walked through seven or eight centuries of painting, downstairs, one floor at a time. Notice how the Madrid light outside looks now... perhaps a little more like a painting than it did when you arrived.