More than any other American building, the home of the Yale School of Architecture holds a special, numinous place in the hearts of architects throughout the world. Recently, in the final stages of its being overhauled, journalists and critics were taken on a hard-hat tour of the premises by the school’s current dean, Robert A.M. Stern, and by Charles Gwathmey, who has designed its new annex.

Paul Rudolph’s imposing Art and Architecture Building is nothing less than the physical embodiment of the institution that inhabits it, and that institution is very likely the most influential school of architecture since the Bauhaus of the 1920s. Some of contemporary architecture’s foremost practitioners have studied there, among them Sir Norman Foster, Sir Richard Rogers, David Childs, and Maya Lin. And some of the most important architects of the past — and the present — have taught there, among them Louis Kahn, Frank Gehry, Peter Eisenman, and Mr. Stern, himself an alumnus.

Without question, this Brutalist pile, completed in 1963, is an icon of the Modern movement, a place, a site, that remains awash in sentiment for all those driven spirits who, at the outset of their careers, toiled within its concrete warren. To listen to some of them, you would think that it incarnated nothing less than the spirit of Architecture itself.

That is hardly to say that it is universally loved. Much of it was gutted as a result of a suspicious fire back on June 14, 1969, in what may have been the single most incendiary act in the history of architectural criticism. Like a man who has survived an assassination attempt but is never quite the same thereafter, the building was subject, in the ensuing decades, to a series of restorations and revisions so maladroit that Rudolph (1918-97), a notoriously cantankerous character, could claim that it “no longer exists for me.”

In order to rectify those revisions and to address the school’s insatiable need for more space, Yale enlisted one of its most eminent alumni, Mr. Gwathmey, to restore the interior to something like its original state. In addition, he has designed, on its northern flank, an entirely new building that will comprise the Jeffrey Loria Center for the History of Art and the Robert B. Haas Family Arts Library.

When it reopens on November 9, the original building will be officially renamed Paul Rudolph Hall, in honor of the charismatic figure who not only designed it, but ran the entire school as his personal fiefdom between 1958 and 1964. Rudolph was the sort of polarizing figure who, both in his pedagogy and in his practice, inspired an equal measure of devotion and ill will. Even today the building remains obviously and instantly controversial. But 45 years ago, at its inauguration, it possessed the fury of a polemic. A sullen gray megalith fashioned out of corduroy concrete, this bully of a building was perhaps the first on our continent to introduce the more subjective, Brutalist aesthetic that Le Corbusier had developed in the postwar period. To a culture that, for two decades, had been fed a mortifying diet of glass and steel, the abrupt intrusion of so much raw emotion was a shock to the system.

But because Rudolph was a very different architect from Le Corbusier, his brand of Brutalism was very different as well. The familiar Modernist grid has been fractured and mangled at Yale, but not fundamentally abandoned, as Le Corbusier had done at Ronchamps. Above all, Rudolph acquired from his predecessor’s late style a knack for thinking volumetrically, rather than modularly, as most earlier Modernists had done. Especially in the famous photographs by Ezra Stoller, the building’s eastern façade stacks up to create a jaunty, ad hoc symmetry. Meanwhile, its vertiginous tangle of interior spaces, occupying fully 31 different levels, was literally improvised from the ground up as each level was under construction. Perhaps it will come as little surprise that the result was more aesthetic than functional. Compared to contemporary architectural practice, it was like a gas-guzzling Studebaker next to a post-industrial Lexus. Its labyrinthine spaces baffled even its most inveterate inhabitants, who had to wear mittens in winter and next to nothing in summer, all the while treading very carefully indeed while rounding the stairwells, with their low-lying banisters.

Just as Rudolph was different from Le Corbusier, so Mr. Gwathmey is different from Rudolph. He is a diplomat among architects, whereas Rudolph was a mud wrestler. Mr. Gwathmey’s stock in trade is smooth legatos of movement through space, gently undulating forms, muted colors, and refined details. In an architectural age in which shock and awe are now tepidly expected, it is unlikely that any building could achieve the response that Rudolph’s building inspired 45 years ago, and Mr. Gwathmey, probably wisely, has not even tried. In part he had the unenviable task of designing a co-equal counterpart to the pre-existing structure, since it is highly doubtful that anything would make eminent visual sense while standing next to it. In the event, the new structure invokes the spirit of the earlier building through its own syncopated surface of straight lines and right angles in two tones of gray. Like most American architects, Mr. Gwathmey is not as aggressively volumetric as Rudolph was, and the deconstructed flatness of his façade reads like a gentle corrective to the truculent protrusions and recessions of the older building.

However that may be, there is reason to be confident that, when the renovations of the old building and the construction of the new one are completed in a few months, Yale’s Art and Architecture Building will be far more amenable to human habitation than it has ever been before.