Revisiting the National Gallery of Art’s East Building, which reopened Sept. 30 after a three-year renovation, is like greeting an old friend. She still has all the same familiar qualities, and conversation picks up as if no time has passed at all. But you also can’t help but notice: She looks good.

The I.M. Pei-designed wing of the National Gallery, a monumental presence on the Mall, opened in 1978 with its geometric peaks and knife-sharp edges — one, at a 19-degree angle. Its collection picks up where the West Building, which features art from the 13th through 19th centuries, leaves off: Here, you’ll find the gallery’s modern and contemporary art, as well as special exhibitions. After nearly 40 years, the building needed upgrades to both improve infrastructure and accessibility and to make room for the museum’s expanding collection.

“We knew we needed to find something that would work within the Pei vocabulary,” said Mary Katherine Lanzillotta, a partner at Hartman-Cox Architects, which oversaw the renovations. That meant sourcing Pei’s original materials and echoing the lines of the building’s interlocking triangular shapes. The renovations cost $69 million, financed with $39 million in federal funding and a combined $30 million donation from local philanthropists.

There are bright, airy, contemplative new spaces for art and new pathways throughout the East Building, which is, itself, an architectural masterpiece. Let’s get reacquainted.

What’s new?

More space for the permanent collection. One of the biggest upgrades was the allocation of more exhibit space in the existing five-story building. The renovations added 12,250 square feet, allowing for the permanent-collection works on display to be increased from 350 to more than 500. Much of that new space is in the museum’s three skylight-topped towers, two of which are connected by a new rooftop terrace.

The new spaces also have changed how visitors move through the museum. The permanent collection begins on the mezzanine level, where special exhibitions used to be displayed. Because the renovation better connects the exhibition spaces, curators are able to present the collection in chronological order.

“It’s hard to tell a story in fragments,” said associate curator Molly Donovan. With the permanent collection’s new presentation, she added, “we’ve been able to tell a more complete story.”

On the mezzanine, you’ll start with Picasso and Matisse circa 1900, and work your way through modernism, cubism, Fauvism and German expressionism. Then it’s one flight up to early abstraction, Dada and surrealism, postwar European art, abstract expressionism and pop art.

There’s a special exhibition on this upper level, “Photography Reinvented,” and, on the mezzanine, a display of recent artworks donated to the museum — all in striking monochrome. A small black box theater has been carved out of this space to show video, beginning with James Nares’s “Street.”

In the towers — two are new to the public — curators have honed in on individual artists. Tower one, at the easternmost point of the building, is divided: On one side, visitors enter to Barnett Newman’s “The Stations of the Cross” and, on the other, to a collection of Mark Rothko works. Tower two was designed to display Alexander Calder’s stabiles and mobiles, suspended from the skylights. Those towers also house parts of the permanent collection, but tower three features a special exhibition of Barbara Kruger’s work. The gallery immediately below it displays Henri Matisse cut-outs.

On the ground level, there are newly configured galleries. One, on American art from 1900 to 1950, focuses on George Bellows, Edward Hopper, Georgia O’Keeffe and Alfred Stieglitz, among others, and another has updated the museum’s popular exhibition of small French paintings. Think Braque, Picasso and Bonnard, as well as a stunning room devoted entirely to Modigliani. These works, said curator Harry Cooper, “have the carved frames that go in the West Building, but they’re really East Building paintings.”

On the underground concourse level, you’ll find a special exhibition gallery housing the temporary show “Los Angeles to New York: Dwan Gallery, 1959-1971,” as well as a collection of contemporary art. They’re organized thematically: One space is dedicated to art that pertains to “markers and signs,” including Jasper Johns’s “Target.” Another grouping of objects relates to “flow,” whether the flow of water or air depicted in a work, or the flow of paint across a canvas. It’s “the idea that art isn’t static,” Donovan said. “It’s always moving.”

Stairs: The stairs are symbolic of the entire project. In Pei’s original building, the floors in the towers were connected by steep spiral staircases. They were part of his vision but also tricky to navigate. Architects have replaced them with stairways that follow the triangular lines of the building, with more landings to make them easier to climb. They also connect the building from top to bottom; previously, only certain galleries were stair accessible.

“These staircases enable the visitor to make new connections between different eras in art,” Donovan said. “We’re not putting people on a singular path. They can make their own pathways.”

Only one set of Pei’s stairs remains, in tower three — they lead to the temporary gallery with the Kruger exhibition. And there’s a new, enormous elevator in tower two that will better facilitate the moving of large artworks.

Floors: Some of the flooring, including in the stairways, was cut from the pink Tennessee marble that was used originally. For historical accuracy, the stones had to be cut from the same quarry, and they were carefully chosen and arranged.

“The stone matching — it’s almost like fitting a dress or tailor-making a suit,” said Susan Wertheim, deputy administrator for capital projects.

In the galleries, new floors made of fumed oak bring a golden warmth to rooms where there was once dark carpeting or concrete.

Works from the Corcoran: The National Gallery acquired more than 6,000 works from the Corcoran Gallery, and many favorites can be seen in the opening installation. More than 40 pieces from the former museum are on display in the permanent collection, as indicated by their tags. Some of the major acquisitions on display include the crimson monolith of Anne Truitt’s “Insurrection” (in the “minimal, post-minimal and conceptual” room), Jenny Holzer’s scrolling-text “Truisms” (in the “Flow” room), Bruce Nauman’s neon word art “Sweet Suite Substitute” (in the “Markers and Signs” room) and George Bellows’s “Forty-two Kids” (in the American art section).

Roof terrace: Once you’ve climbed to the top of towers one and two, be sure to head outside onto the new outdoor exhibition space, where you’ll be able to gaze over Constitution Avenue alongside a nearly 15-foot electric blue rooster. The sculpture, “Hahn/Cock” by Katharina Fritsch, was created for London’s Trafalgar Square and is on loan from the Glenstone Museum in Potomac. It’s joined by other works, including Nam June Paik’s “Ugly Buddha” and “Ugly TV.”

Cafe: The museum has reopened the terrace cafe, which is connected to the upper-level galleries by a bridge. The cafe offers views of the 76-foot-long untitled Calder mobile hanging in the atrium, turning gently in a way that belies its massive weight.

“The presence of the Calder — you can feel how radical that is, it’s like seeing a ship come into harbor,” Cooper said.

The museum’s food service is being run by a new operator, Starr Restaurant Group, which revamped the menus of every National Gallery cafe. The Terrace Cafe will offer coffees and pastries, with grab-and-go salads and sandwiches costing $8 to $10.

Finding your favorite works

Want to see some of the East Building’s most famous works in their new digs? Here’s where to find them.

Pablo Picasso, “Family of Saltimbanques,” 1905. This painting of poor circus performers, which Hopper calls “the first great painting of the 20th century,” is front and center as you enter the permanent collection on the mezzanine level.

Jackson Pollock, “No. 1, 1950 (Lavender Mist),” 1950. This painting commands an impressive room of abstract expressionist work on the upper level.

Glenn Ligon, “Double America,” 2012. Ligon’s neon piece, a reflection on race and politics, seems to be the perfect metaphor for this year.

Andy Warhol, “A Boy for Meg,” 1962. Warhol’s painting of the Nov. 1, 1961, New York Post front page is exemplary of his fascination with celebrity and consumer culture.