Under the stewardship of departing director Thomas Krens, the Guggenheim has become the cosmopolitan highflier of New York museums, with new branches in Bilbao, Spain, and Berlin, and visions of others in a startling number of locations: Lower Manhattan, Las Vegas, Taiwan, Hong Kong, Rio de Janeiro, Mexico, Lithuania, and Abu Dhabi. Guggenheim outposts operated for several years in the first two places.

A branch three times the size of the Bilbao museum is slated to open in Abu Dhabi in 2011.

Some of the most reliable rewards of the flagship museum on Fifth Avenue, however, have been its most traditional art — the Thannhauser Collection of Impressionist and Post-Impressionist paintings, installed since 1965 on the second floor. Following a renovation of this space, nearly 30 of the more than 70 pieces in the collection are again on view. This means that no matter what awaits visitors at the top of the spiral, they can again rest assured of the pleasures of Cézanne, Degas, and Picasso below.

The Thannhauser bequest represents just one of several significant additions over the last several decades to Solomon Guggenheim’s original collection of “Non-Objective” art. It was, however, the first, and the only one requiring the work to be permanently on display in a designated space. It also radically broadened the initial scope of the museum’s holdings. As Time magazine noted of the newly acquired paintings, “in one stroke they make the Guggenheim a showcase for modern art.”

A few years after taking over his father’s Munich gallery in 1921, Justin Thannhauser opened a second branch in Berlin. By the time the Berlin gallery closed because of the gathering Nazi threat, the Thannhausers had brought before the public an astonishing assortment of avant-garde French and German art, including the very first exhibition of Der Blaue Reiter and the most comprehensive surveys to date of Matisse and Picasso.

The collection bequeathed to the Guggenheim reflects a considerably smaller range of artists, all of them French (save Picasso, Klee, Pascin, and Van Gogh) and only Picasso — a family friend — is represented in great depth. Many of the other artists, though, are represented by particularly choice works. With the new installation, visitors can again savor Pissarro’s sunlight-charged “The Hermitage at Pontoise” (c. 1867), the largest canvas he ever painted. Van Gogh’s “Mountains at Saint-Rémy” (1889), too, is back. Painted only a month after the celebrated “Starry Night,” its churning colors show the same mixture of earnestness and exuberance. Seeing it afresh, visitors may be struck by the daintiness of flowering plants in the foreground. Hung artfully alongside, Braque’s Fauvist “Landscape Near Antwerp” (1906) looks surprisingly potent; the future Cubist’s line is more self-possessed, but his colors no less vivid.

The Guggenheim’s most recent catalog of the Thannhauser collection records how Renoir, some 40 years after painting “Woman with Parrot” (1871), dismissed it as worthless “daub” — a puzzling assessment, considering the canvas’s sumptuous darks and luminous skin tones. (It may be connected to the fact that the model was Renoir’s companion for six years.) Indeed, though more conventional in technique and subject matter, this painting’s rhythms are at least as muscular as those of the two rather wispy Manets flanking it on either side; these images of women in interiors suggest that the Impressionists gained more from Manet’s influence than he did from theirs. The date (1908) of Monet’s glowing view of Venice highlights the caprices of history. The previous year, Picasso’s “Les Demoiselles d’Avignon” had signaled the ascent of Cubism.

Familiar works by Degas, Vuillard, Gauguin, Toulouse-Lautrec, and Henri Rousseau fill out the new installation. Picasso’s “Le Moulin de la Galette” (1900), however, truly presides. This canvas — his first Paris painting, produced when he was only 19 — stuns with its easy mastery of color and drawing. The variety of hues, within both lights and darks, captures the sheen of top hats as authoritatively as the glare of lamps. The animated verticals of the dancers culminate in an evocative horizontal flicker of lipstick, eyelashes, and hats. Other works showing off Picasso’s protean gifts include the somber-toned “Fernande with a Black Mantilla” (1905-06), with its veils of dribbled paint, and the “Head of a Woman (Dora Maar)” (1939), in which the wood grain of the painting’s support hardly registers amidst the effervescent swellings of blue and orange.

But if Picasso supplies the collection’s libido, Cézanne provides its heart. Among four of his canvases now on view, the thinly painted brushstrokes of “Bibémus” (c. 1894-95) seem like ephemera — mere testings and notations. Yet they accrue with bulldog force, spelling out the momentous breadth and height of a sandstone bluff. In the far denser, darker “Still Life: Plate of Peaches” (1879-80), boulder-like fruits adorn a plate. Below, a single nick in the hem of a tablecloth paces out its horizontal passage. With such paintings, Cézanne planted himself at the crossroads, intimating what Picasso later broadcast: the abstract process connecting perception and representation. Today we may marvel at how perfectly they enlarge the Guggenheim’s original mission, several incarnations ago, when it was known as the Museum of Non-Objective Painting.

Opens June 28 (1071 Fifth Ave. at 89th Street, 212-423-3500).