Few architectural projects in recent history have been so famous, and notorious, as the great glass pyramid at the Louvre in Paris, designed by the American firm of Pei Cobb Freed & Partners. It has been hailed as a triumph and condemned as a desecration, or worse. And yet, willy nilly, it has become a potent new symbol of the city, rivaling the Eiffel Tower.

Although clearly there's no substitute for seeing the thing itself, Washingtonians in the next few months will have a splendid opportunity to better understand the $1 billion project. Which, on the evidence somewhat haphazardly presented in a major exhibition, "The Grand Louvre: Entering a New Century," one would have to say has been rather misunderstood.

The exhibition contains more than 150 drawings, prints, photographs and models, and it takes up all of the limited space available at the Octagon Museum plus a good bit of the first and second floors of the nearby American Institute of Architects headquarters. In reality, it's two shows. One, at the Octagon, tells the 800-year story of the palace-museum; the other, spilling over to the AIA, concentrates on the Pei firm's work.

An important lesson of the second show is that the pyramid, upon which both praise and ire have been focused, is simply the tip of the iceberg of this demanding architectural job. It is an impressive object to be sure, a bold contrast to the rich Renaissance surroundings of the Cour Napoleon, the huge open courtyard of which it is now the centerpiece. There are models of it here, and abstract drawings and lovely nighttime renderings and tautly engineered steel parts -- all take one's breath away with their precision and beauty.

Even so, these pieces don't quite add up to a convincing picture of the whole thing, of the spaces it defines and its real-time, real-life presence. What comes through strongly from a patient perusal of the mountain of material in the show are the most excellent reasons for its being where it is and what it is. The pyramid is the apex of a brilliant strategy not only to restore the Louvre but to improve it vastly.

The striking object is, for starters, a new main entryway to the museum -- a fact that helps both to explain and to justify its transparency and dramatic form. Its physical separation from the old Louvre buildings makes possible a thoroughly uncompromising restoration of the historical facades. Even more important is the fact that most of the construction is taking place underground (the project won't be completed for another two years), to accommodate cars and buses, museum services and storage, and public functions other than viewing art. This will permit the museum to more than double the space available for exhibitions in the old buildings.

This is truly an exhilarating prospect. Self-evidently the Louvre is one of the world's fabled art repositories, but it will be utterly transformed when this project is done -- its collections more fully and more logically displayed, its galleries more numerous, more spacious and better lighted. This revitalization will include a complete rebuilding of the interiors of northern wings that formerly housed the Ministry of Finance; the courtyards there, once accessible only to bureaucrats, will be turned into great skylit spaces for the display of sculpture.

There is more good news to come. Those of us who fondly remember hours and days spent soaking in the lessons of the museum's nonpareil masterpieces also recall the many closed doors and the long, off-putting facades along the Rue de Rivoli. From the outside, the Louvre has long been something of a rudely closed book. The Pei firm's site plans, with new pedestrian openings and automobile traffic shuttled efficiently underground or pleasantly on the surface, will decisively change these conditions. The "new" Louvre will be attached to the surrounding city as never before.

It becomes obvious, then, that the Grand Louvre project is much more than a matter of plopping a jewellike contemporary object in the middle of a plaza. Whatever one ultimately thinks about the pyramid, one must recognize it as the symbol of an incredibly ambitious, complicated task of architecture and planning, undertaken with daring, intelligence and skill. Louvre Director Michel Laclotte, who was in Washington this week to lecture along with I.M. Pei and members of his redoubtable design team, asserted that despite the clear contrasts between old and new, the project represents "a kind of continuity ... with what could be called the tradition of the Louvre."

And how. The Louvre was of course a royal palace long before it became a museum, and its history has been one of almost constant change and enlargement. The palatial complex of buildings indeed has been a stage upon which has been played out the ambitions of the greatest of French kings and the talents of the nation's best architects. This story is laid out in fascinating, though occasionally befuddling, detail in the Octagon exhibition.

Among the displays are engravings that enumerate the profusion of plans for the Louvre's completion over the centuries; period maps showing waves of construction and destruction; surprising bird's-eye views demonstrating how, even after the 16th century, the medieval-type city would spread onto the royal turf, only to be demolished again; elevations and plans by practically all of the architects who contributed to the Louvre over the years (and by many who wanted to, but who were ignored or fired); scale models of the complex at various critical stages; and much more.

Of special interest, in the context of the Pei effort, is a series of designs made in the 17th century by the Italian architect and artist Bernini at the behest of the young Louis XIV. One of these, showing the east facade as a great, graceful semicircle, is truly representative of the artist's genius, but it offended French taste and was dismissed -- as was Bernini, in short order, by the Sun King himself, who gave the job to a Frenchman. Something of the same kind of chauvinism greeted President Francois Mitterrand's selection of an American architect for the Grand Louvre project in the early '80s. But according to one of last week's visitors, at a critical moment back then the Socialist president whispered to I.M. Pei, "What happened to Bernini won't happen to you."

How fortunate, it now seems clear, that the president kept his word.

"The Grand Louvre: Entering a New Century" was curated by Judith Schultz Nyquist and organized by the American Architectural Foundation as part of its annual "Accent on Architecture" celebration. The Octagon is at 1799 New York Ave. NW, and the AIA at 1735 New York Ave. NW. The show will remain on view through May 21.