The Met Cloisters audio guide,
five stops, free.

Bend a little closer than feels polite. The whole altarpiece, open, is about a metre and seventeen centimetres wide, and the middle panel is barely sixty-four centimetres square. It was never meant for a church. It was made for a fifteenth-century family to pray in front of at home, and the late medieval furniture around you was chosen to echo the objects in the picture.

The centre panel is the Annunciation, set not in a temple but in a comfortable house of the painter's own day. Mary sits on the floor in a red gown, lost in her book. The angel Gabriel has just come in and is about to speak, and she has not noticed him yet. Now look at the round window at the upper left. Golden rays come through it, and riding down them is a miniature figure carrying a cross. That is the Christ Child, on his way. On the table, a candle has just gone out. The wick is still glowing and a curl of smoke is rising from it. A lily stands in a jug beside it.

On the right wing is Joseph, a carpenter, drilling holes in a board. On his bench sits a mousetrap, and there is another set out in his shop window facing the street. It is a joke with a theological point. Saint Augustine wrote that the cross was the devil's mousetrap, baited with the death of Christ. In 1966 a scholar argued that the thing on the bench was really a carpenter's plane. That same year a museum man in Liverpool, John Jacob, had the trap built from the painting and caught a mouse with it.

On the left wing, the man who paid for all this kneels in the garden, peering through the open door at the miracle as if he had been let in by accident. His wife kneels behind him. She was not in the first version. The Met's reading is that the centre panel came first, probably painted without a commission, that the donor then ordered the wings, and that in the 1430s, presumably after he married, his wife and the messenger at the gate were added. Even the sky behind Mary is a revision. Those windows were gold leaf until someone painted them blue.

The painting comes from the workshop of Robert Campin in Tournai, sometimes called the Master of Flémalle. Documents say he hired at least two assistants, and one of them was the young Rogier van der Weyden. An earlier, damaged version of the centre panel survives in Brussels and may be Campin's own.

It takes its name from the Mérode family, Belgian aristocrats who owned it in the nineteenth century. It spent generations in private hands, seen by almost no one, until 1956, when John D. Rockefeller Junior funded its purchase for this building. People called it a major event in the history of collecting in America. The Met calls it one of the most celebrated early Netherlandish paintings, and part of the reason is simply condition. After six hundred years, that curl of candle smoke is still sharp enough to see.

Stand under the arcade for a moment and look at the colour of the stone. Pink, streaked with white, warm even on a grey day. This is the heart of the building, and it was meant to be. A cloister was the heart of a monastery too: a covered walk around an open garden, with a door to everything else. Monks walked it in procession, read aloud in it, meditated in it, and did their washing here, clothes and themselves.

These capitals come from the Benedictine abbey of Saint-Michel-de-Cuxa, at the foot of Mount Canigou in the Pyrenees, founded in 878. In 1791, in the wake of the French Revolution, the monks left, and the stones were carried off and scattered. The original cloister was about twice the size of this one. George Grey Barnard, an American sculptor who collected medieval stone in France, bought what he could find, reportedly for a hundred thousand dollars, and brought it to New York. Part of the cloister is still in France, and so, again, are monks. There is a community living at Cuxa today.

Here is the surprise. Not everything you see is medieval. The Met counts some four hundred and sixty original fragments, including thirty-six capitals but only twelve of the shafts that hold them up. Everything missing was cut new, in the same pink Languedoc marble, from a quarry near Cuxa that was reopened in the early twentieth century for exactly this purpose. Old and new are the same stone, so your eye cannot sort them. Look for the little diagrams at the corners of the walkway; they show you which is which. The low wall under the columns and some of the arches above are the reconstruction. The carved tops are the real thing.

So walk around and read the capitals. Some are plain blocks. Others are thick with scrolling leaves and pinecones, with lions eating people or gnawing their own front legs, and a mermaid holding up her tail. At the corners, look for animals with two bodies and one shared head, a design worked out to wrap round the edge of the block. Nobody knows the order the capitals stood in at Cuxa, so there is no story to follow from one to the next, and the Met suggests the carvers cared less about meaning than about energy, the tension of bodies pressed into stone.

In the garden the paths cross at a fountain, the typical plan of a cloister garden. In spring and summer it is full of flowers and the air smells of lavender, which is exactly the effect the people who built this place were after.

After the tapestries and the stone, this will feel tiny. The Cloisters Cross is fifty-seven and a half centimetres tall, carved from walrus ivory, and it carries ninety-two figures and ninety-eight inscriptions across its two faces. The figures are about a centimetre high. The Met calls its programme of images unrivalled in Christian art, and it is worth getting as close to the glass as you can.

On the front, the shaft is carved as the trunk of a tree laid over the cross, so that the cross becomes a living thing. The square plaques at the ends show scenes of the death and resurrection of Jesus. On the back, Hebrew prophets hold scrolls with their own words written on them, around a central medallion of the Lamb of God, which appears to be pierced by a figure personifying the Synagogue. The ends of the back carry the symbols of the Gospel writers: the lion of Mark on the left, the ox of Luke on the right, the eagle of John at the top. The bottom, where the angel of Matthew belonged, has been lost.

The cross is usually called English, carved around 1150 to 1160, and it has often been linked to the abbey of Bury Saint Edmunds in Suffolk, though some scholars think it more likely came from central Europe. Its inscriptions are the uncomfortable part, and the Met does not hide them. Several are strong attacks on Jews. The ivory figure of Christ that once hung on it is lost, but the sign at the top of the cross survives, and where the Gospels have it read King of the Jews, it has been changed to King of the Confessors. The museum's own reading is that the cross reflects the hostility to Jews widespread in England at the time; by the end of the thirteenth century they had been expelled from the country.

How it got here is a thriller. Nothing is known of it before it surfaced with Ante Topić Mimara, a Croatian collector. The British Museum wanted it but held back because he could not prove he had full title to sell it. Thomas Hoving, then associate curator here, reportedly sat up drinking coffee with Mimara until the British Museum's option ran out at midnight, and bought it on the spot for six hundred thousand dollars. It entered the collection in 1963. For an object that came down to a midnight deadline between two of the world's great museums, it is small enough to hold in two hands.