Seen from above the quayside, across the slowly moving waters of the Schie river full of dark reflections, the distant centre of Delft is hit by early morning sun. Soon people shall be walking its streets, with their yellow cobbles and freshly washed tiles, as children play by front doors and servants go about their work, glimpsed in the gloom of a side alley. Opening the magnificent Johannes Vermeer exhibition at Amsterdam’s Rijksmuseum, two paintings of these morning scenes plunge us right in, taking us on a journey through Vermeer’s art, spread across 10 rooms. We shuttle from city views to private interiors, between the sacred and the profane; from domestic life, with quiet music and private moments, to religious devotion and bawdy scenes. All this in an exhibition of only 28 paintings. These were created in 20 years, between 1654 and 1674. There are only 37 known paintings by Vermeer. A few are contested, an unknown but probably small number long lost, and one was stolen from Boston in 1990 and has never resurfaced. A few paintings can’t be lent. The Vienna Kunsthistorisches Museum dithered over lending The Art of Painting (1666-68), eventually refusing to loan one of its star exhibits. This is the most important omission here, in what is the largest ever show of Vermeer’s work. The last big Vermeer show, in The Hague, was a febrile, crowded experience. Here, the art has room to breathe. A girl reads a letter, her vague reflection caught in the angled windowpane. There’s a rumpled carpet on the table in the foreground between her and us, and on it a tilted bowl of fruit catching the daylight. One green apple appears as big and round as her forehead. On the wall behind is a picture of a naked Cupid, looking back at us. This picture-within-a-picture knows we are looking – and knows we know, too, while the girl herself believes she is unobserved. The situation is redoubled by the fact that this painting, Girl Reading a Letter at an Open Window, also hangs in a small room on its own, and we are there with her. Elsewhere, a milkmaid is pouring milk and preparing a basket of bread. She is alone in the kitchen, a situation somehow emphasised by the blank wall behind her, pockmarked by little craters and scuffs in the plaster, and the bare nail sticking out of the wall that casts its shadow above her head. Such a little thing, on a wall luminous with daylight. A workspace then, where you could hear the sound of the pouring milk and smell the granular crust of the bread and its tufts of crumb. I understand this homely scene not just through sight, but also through the milkmaid’s senses. It is an invocation of the ordinary, elevated to the marvellous. Our being there with these women, unaware of being seen, feels like a kind of privilege, as we encounter them in their solitude, absorbed in their occupations. The exhibition is filled with such moments, guiding us through Vermeer’s career just as the artist himself guides and directs us through his painted scenes. The eye skips and darts about, but Vermeer manipulates us at every turn, drawing things in and out of focus, glossing over some things, bringing others to the fore. All the details in his art may be acutely observed – from the clouds passing over Delft to the finial on a Spanish chair, the burr on an Anatolian carpet and the glint on an earring – but they are more than inventories of the visible. Although a devout observer of the surface of things, which he became within a few short years, Vermeer was not a realist. His paintings are careful, complex constructions. Their meticulously crafted artifice is all fiction and allusion, tempered by both worldliness, curiosity and the Catholic faith to which he converted on his marriage. And Vermeer certainly never sat in a camera obscura, copying the inverted image projected on the darkened wall. He was no copyist, although, influenced by the Jesuit scientific and quasi-religious interest in optics, he understood and was interested in the way light illuminated objects in a camera obscura – and used its effects, just as he used single-point perspective to measure and construct the architecture of his painted spaces. Artists are always interested in whatever technology they have to hand. Vermeer wanted to see more, by whatever means. It is impossible for us to look at his art without thinking of photography and film-making: Vermeer pans out and zooms in, keeps us on the threshold and snags us with details that reveal themselves over time. In The Love Letter, a maid has just brought her mistress a letter which they are discussing avidly. We seem to be passing in front of the doorway, like guests infringing on a private moment. The maid’s clogs, bucket and mop are abandoned on the threshold. These objects seem to have been left in a hurry. We are not meant to step over them. Vermeer’s art is full of such details and complexity, whether it is the light crossing a wall, a dancing reflection in a wine glass, the tiniest sliver of a view at the edge of a window, a human drama played out in front of us. There is nothing trivial here. He also directs us to things we can never know: people are always concentrating on unreadable letters, or looking beyond the picture’s edges or through windows at things we can’t see. They play unknown music and hold conversations we can never eavesdrop on but only surmise. We are kept on the brink, sometimes teetering. A man looms beyond a seated girl, holding a jug of wine. His face half-shadowed, he waits and watches her drink. You sense his power, her passive and perhaps unwilling compliance. A woman holds her necklace, stilled in thought and staring into the light through the window. She’s a girl interrupted and lost in thought. But it isn’t all such great work, nor as compelling. Vermeer’s early painting of Saint Praxedis, wringing the blood from a severed martyr’s head into a jug, is a copy of an Italian painting. The modelling of her head is somehow slithery and strange, the colour largely flat and cumbersome. The anatomy of Diana and Her Nymphs is awful (no wonder the Dutch forger Han Van Meegeren chose this phase of Vermeer’s art to concoct his frauds in the 1940s). Vermeer’s later Allegory of the Catholic Faith, meanwhile, is a swooning monstrosity. Only the closely observed details work. Even the glass sphere dangling overhead – a Jesuit symbol of inner light and the expansiveness of the unbound soul – appears to be based on observation rather than a fervent invocation of the transcendent; its little blips of refracted and reflected light are wonderful. Mystery and enigma are attractive. Who is that woman in the red hat, or the one with the pearl earring? What’s in that letter? What is that girl looking at through the window? What is she thinking? Who is approaching? This exhibition, at last, gives us not just Vermeer’s painted spaces, but space to be with them and to occupy their unfolding strangeness. Unmissable.