Gemäldegalerie Alte Meister audio guide,
five stops, free.

Two green curtains have just been pulled back, and everything behind them is happening in mid-air. That is the trick of this picture, and it works from the far end of the room. There is no floor, no throne, no architecture. The Madonna is walking towards you on cloud, barefoot, carrying a heavy child, and the only solid thing anywhere is the wooden ledge along the bottom edge, where two small winged boys are leaning on their elbows, looking up, thoroughly unimpressed.

You know those two. They have been on stamps, postcards, T-shirts, socks and wrapping paper for more than a hundred years. As early as 1913 the writer Gustav Kobbé said that no group of cherubs anywhere is as famous as the two that lean on the altar top at the very bottom of this picture. Most people who could draw them from memory have no idea what is above them.

What is above them is Raphael, near the end of his life, working for Pope Julius the Second. Julius commissioned it in 1512 in honour of his late uncle, Pope Sixtus the Fourth, for the high altar of the monastery church of San Sisto in Piacenza, south-east of Milan, and the commission required that two particular saints appear. Sixtus is on the left, the old man in gold, pointing out of the picture with his right hand. Barbara is on the right, looking down. Behind the Madonna, in what reads at first as pure light, are dozens of half-visible faces of other angels.

It reached Dresden in 1754. The Saxon court had been negotiating for nearly two years through an agent called Giovanni Battista Bianconi, and Augustus the Third paid somewhere between a hundred and ten and a hundred and twenty thousand francs, which stayed the highest price ever paid for a painting for decades afterwards. The story goes that he moved his own throne to give it a better wall. In 1855, when Gottfried Semper's new gallery opened, this canvas was given a room of its own.

Then the twentieth century. In the war it went first to the Albrechtsburg at Meissen, then in 1943 into a disused railway tunnel at the Lohmgrund near Rottwerndorf. In July 1945 the Soviet trophy organisation took it to Moscow, where it stayed for ten years. A legend grew up about soldiers wading knee-deep through a flooded cave, carrying the Madonna slung on cloths. In 1991 the Russian art historian Andrei Chegodaev, who had been sent to Germany in 1945 to look at the art, called that story the most insolent, bold-faced lie. The picture had been in a dry tunnel with instruments monitoring the humidity, and it was in its frame, and no four men could have lifted it that way. It came home to Dresden in 1956.

One more story, from 1849. During the Dresden uprising, Mikhail Bakunin is said to have advised the revolutionary government to carry the Sistine Madonna out of this building and hang it on the barricades at the edge of the city, on the theory that the Prussian troops were too cultured to fire on a Raphael. Nobody took him up on it. Now look back down at the two boys on the ledge, and decide for yourself whether they are listening.

Vermeer was twenty-four. This is the first picture in which he painted the world he actually lived in instead of a Bible story or a myth, and you can feel him working out what kind of painter he is going to be.

Four people in a row, pressed up against the front of the canvas. On the right a young woman in a yellow jacket and a white headdress, smiling, holding out an open hand. A soldier in red has one arm around her and the other at her breast, and he is dropping a coin into her palm. Behind them a woman in black leans in, watching the money. And on the far left a man in a black beret and a doublet with slashed sleeves raises a glass and grins straight out at you.

That man has been identified as Vermeer. The face resembles the painter seen from behind in his Art of Painting, and whoever he is, he is looking straight at us.

Now look at the bottom half of the picture, because that is where most of the work went. A carpet takes up a third of the canvas, thrown over a banister. It comes from Uşak in western Anatolia, and the dark blue ground with its red onion-shaped medallion dates the type to the first half of the sixteenth century. The blue and grey jug sitting on it is Westerwald stoneware. The instrument in the left-hand man's other hand is probably a cittern. And the dark coat with five buttons in the foreground was not there at first; Vermeer added it at a later stage.

This is one of only three paintings he ever signed and dated. The other two are the Astronomer and the Geographer. When it came up at auction in Amsterdam in 1696 it was catalogued simply as a merry company in a room. Dresden bought it in 1741 out of Count Franz Josef von Waldstein's collection at Dux in Bohemia, for the Elector of Saxony, and it went to Moscow with the rest of the gallery in 1945 and came back in 1956.

One footnote, because it is a good one. There is another Procuress that was attributed to Vermeer for years, until technical analysis in 2011 found Bakelite in the paint. It was almost certainly made by Han van Meegeren, the forger who hardened his fakes with resin. This one, with the coin and the carpet and the man grinning over his glass, is the real thing, and the paint is 370 years old.

No shadows. That is the first thing, and it becomes strange once you have noticed it. A figure standing in a room that throws no shadow anywhere, against a pale wall and plain floorboards, with nothing else in the picture at all except what she is carrying.

Francesco Algarotti, the Italian writer who bought it, saw that straight away. He wrote to his friend Pierre-Jean Mariette in 1751 that the picture is almost devoid of shadows, that the light is furnished by two windows reflected in the glass of water, and that although it is a European picture it could appeal to the Chinese, who, as he put it, are sworn enemies of shadows. He also called it a Holbein in pastel. He had bought it from Liotard in Venice on the third of February 1745, acting for Augustus the Third, King of Poland and Elector of Saxony, and it has been in Dresden ever since.

It is not a painting. It is pastel, dry chalk, on parchment, 82.5 centimetres by 52.5, which is why it lives behind glass and why its survival is slightly improbable. During the Second World War it was moved to the fortress at Königstein, sat out the cold and the damp there, and was carried back to Dresden as the German army retreated.

Look at the tray she is holding. Both the lacquer tray and the porcelain cup follow Japanese models, and the tray has a raised rim so that nothing slides off it. The cup is a trembleuse, a cup made to sit locked into its saucer, and in the eighteenth century that meant chocolate, brewed thick and strong and frothy. Chocolate was still a luxury only the upper class could afford, which is why the museum assumes the cup is on its way to somebody of rank. The word comes from the Aztec xocoatl, and the first cacao beans reached Europe with Hernán Cortés.

Who she is has never been settled. Most of the literature calls her a maid. But an old label on the back of an eighteenth-century reduced copy in a house near London says she is Charlotte Baldauf, the daughter of a Viennese banker, drawn by Liotard while he was staying in the banker's house, and later a countess.

And if she looks oddly familiar before you have read a word of this, there is a reason. In 1862 the Baker's Chocolate Company in America obtained the rights to use her, and around 1900 she became the nurse on Droste's cocoa tins. She has been selling chocolate for more than a hundred and sixty years, and she is still holding the tray perfectly level.