"The Art of Painting," Vermeer's magnum opus, will be in Washington for the holidays.

That summarizing canvas, which the Dutch master completed in 1667, is his most ambitious picture. Vermeer refused to sell it. Four years ago its absence left a yawning hole in "Johannes Vermeer," his phenomenally successful retrospective exhibition at the National Gallery of Art. Though set to be the centerpiece of that memorable show, the painting at the time was found too fragile to move. In certain areas of its surface the layers of its paint had begun to come apart.

That has since been corrected. After many months of labor with microscopes and syringes, conservators in Austria--at the Art Historical Museum, Vienna--have deemed their picture fit to travel.

Yesterday the National Gallery announced that the Vermeer would be shown in its West Building from the day before Thanksgiving to Feb. 6.

Part self-portrait from the back, part 17th-century genre scene, part study of the flow of light, part allegory, too, Vermeer's "The Art of Painting" is a picture about seeing--about his own observation, and history's, and ours.

Vermeer, after his death, was entirely forgotten. When "The Art of Painting" appeared on the market in the early 19th century it was thought to be a picture by Pieter de Hooch. All of that has changed. Though only 35 of his paintings have survived, Vermeer is now acknowledged as one of the great painters of his or any age.

The artist in his studio is a common theme in art, but in "The Art of Painting" the workplace of the painter is an immaculate Dutch parlor, curtained like a stage.

The painter's seated at his easel, in rather fancy dress. He has a paintbrush in his right hand, a mahlstick in his left. The pale northern sunlight pours in from the left, brightens a white wall, and then, to make its passage more palpable, catches on the creases of a crinkled wall-hung map.

It isn't the artist, or the model, it is we who have the privileged place in this composition. The heavy hanging tapestry has just been pulled aside, as if by an unseen hand, to let us see the scene.

The model in blue silk standing at the window is another of the master's beautiful young women, moist-lipped, introspective, modest and serene. But she's not only that. The attributes surrounding her spell out who she is.

She wears a crown of laurel leaves, symbolizing Victory. (Those leaves, 300 years ago, were the green of bay leaves, but their colors in the years since then have drifted into blues.) The trumpet in her right hand (actually a sort of trombone) is the trumpet of the herald, or of the herald angel, an attribute of Fame. The thick book that she holds symbolizes History. The stone mask on the table stands for Imitation. These assembled attributes reveal her identity: She isn't just a model. She is Clio, Muse of History.

When Vermeer was starting out in art in the mid 1650s he painted nymphs and martyrdoms in an Italian manner. But the Protestants of Holland, distrustful of such arias, preferred crisp realities to soft Italian visions. Vermeer's "Art of Painting" is half a scene from real life, half symbolic dream.

All the distinct elements of Vermeer's creativity--his science and his poetry, his glazes and his lenses, his metaphysics and his nationalism, his precise mathematics and serene supernal light--sing together in this rich and justly honored work of art.

He probably used lenses--which let him see his world as if he were looking through the viewfinder of a camera. The drapery in the foreground is peculiarly blurred. The map beyond, in contrast, is depicted in sharp focus. In earlier Italian paintings, say Sandro Botticelli's, every detail is sharp, but that is not how we see. When we peer across the room objects near at hand appear out of focus--as they do in Vermeer's painting. He was the first significant European painter to make a shifting focal plane central to his art.

Vermeer may have learned to see the world through lenses from Anton van Leeuwenhoek. Both men were born in Delft in 1632. Both of their fathers were in the silk business. When Vermeer died, miserable and bankrupt, in December 1675, it was van Leeuwenhoek who served as executor of his estate--and van Leeuwenhoek, of course, was the man who perfected the microscope. Both men thought of sunlight not as insubstantial brightness, but as a substance that could be manipulated with lenses--and with the reasonings of the mind.

It was not until the 19th century--and the development of photography--that Vermeer became famous. It may have been photography that helped the world to recognize the sharpness of his eye.

Some of Vermeer's clarity is bred of mathematics. He was a specialist in the rigors of vanishing-point perspective. In "The Art of Painting" all the lines of sight, and the black-and-white floor tiles, and the painter's gaze as well, proceed to a pinpoint next to Clio's hand. The painter actually stuck a pin there, from which he stretched out threads, and one still can see the pinhole that it left there in the paint.

The picture is in other ways marvelously engineered. It is in part a grid of rectangles (the wall, the map, the tiles, the canvas on the easel, the tabletop, the book), and, in equal part, a set of rhyming angles. The spine of Clio's book and the mahlstick that the painter holds are in precise parallel; so are his right arm and the sharp edge of the table. "The Art of Painting" is a picture perfectly locked in.

But it also is a poem, one in which precision is countered by freedom. The out-of-focus curtain is a kind of sketch in color. Clio's bright-white collar was added to the picture with a single swipe of Vermeer's loaded brush.

And then there is the light, a presence almost granular, which somehow lends this vision its over-arching mood of reverie and rapture and quietude and peace.

Vermeer was both a painter and an art dealer. In the last months of his life--a war with France was raging--he was unable to sell either his own canvases, or those by other artists, and plunged deeply into debt.

His widow, in an effort to save "The Art of Painting" from his creditors, tried to give it to her mother--a bit of sleight of hand that offended the executor, who sued to get it back. It is from the papers filed that we know the painting's name.

"The Art of Painting" will be shown here with the four Vermeers in the gallery's collection. The display, curated by Arthur K. Wheelock Jr., the gallery's curator of northern baroque paintings, is funded by a grant from Juliet and Lee Folger/the Folger Fund.

CAPTION: Johannes Vermeer's "Art of Painting," the Dutch master's most ambitious work.