The new exhibit at the Yale University Art Gallery is that rare example of Yale self-congratulatory spirit anyone can enjoy. “Art for Yale: Collecting for a New Century,” which opened Tuesday, displays 300 highlights of nearly 15,700 pieces acquired by the Art Gallery in the last 10 years, which basically amounts to a centuries-old institution saying: “Look what we got! Isn’t this cool???”

Yes, it definitely is. Since 1998, the gallery has amassed a wonderfully impressive and varied collection of artwork, encompassing everything from Degas to Dada. But the exhibition isn’t just about showing off. “Art for Yale” presents pieces that weren’t able to be displayed recently because of the construction on the Gallery, and more importantly, it tries to present the collection in a way that helps the viewer see old pieces in a new light — “allowing the audience to make connections on their own,” explained Amy Porter, the associate director of communications at the gallery.

This intention is masterfully expressed by the eclectic arrangement of works in the room to the left of the lobby. After being greeted by Eakins and Homer seascapes, I progressed to a wall of artwork centered on the theme of war — Civil War paintings, photographs of Vietnam soldiers and photographs of contemporary war protestors. Passing still lifes, 19th-century furniture, porcelain dishes and multimedia installations, I made my way to cases filled with Egyptian reliefs, Etruscan coins and Incan figurines. Turning around, I was face to face with an ornate mirror hanging above an equally ornate American pier table, flanked by red campaign bandannas for Chester A. Arthur and Grover Cleveland.

The display of African, Asian and early European art achieves the same level of thrilling variety, linked in fascinating ways. Japanese nature scenes from the 1700s are juxtaposed with prints from the 1930s; a Cezanne painting hangs next to a photograph from the same era; and objects from the spectacular Charles B. Benenson Collection of African Art abut Renaissance artwork. In one of the most visually breathtaking sections of the exhibit, an exquisite 15th-century Japanese mandala provides the backdrop to five 16th- to 17th-century Korean and Japanese tea bowls.

The exhibit also contains some spectacular modern and contemporary artwork, including pieces by Matisse, Picasso, Rodin, Max Ernst, Chuck Close and Kurt Schwitters. The sculpture is particularly striking, ranging from the flowingly abstract “Resting Leaf” by Dadaist Jean Arp to Degas’ “Dancer Ready to Dance, with Right Foot Forward.”

Unfortunately, some exciting contemporary works in the exhibition — including “Reichstag” by Andy Warhol and “Southeast View from the World Trade Center II” by Yvonne Jacquette — have been left on display in the permanent collection, marked with a Y on their placards. While their eagerness to point everything out is understandable, the curators’ insistence on including works they weren’t willing to move is a reminder of the somewhat boastful, back-patting aspect of the exhibition.

But mostly this exuberance is beneficial to the exhibit, which overflows into the lobby with wall drawings by Sol LeWitt and pieces of a hand-sewn book by Louise Bourgeois entitled “Ode A L’Oubli” (Ode to Forgetting). A series of pieces by Stewart Davis further open the viewer’s mind by discussing the way an artist’s works develop. These works recycle their own symbols and culminate in a large and vibrant painting with an exclamation point signifying it as the finished product.

In spite of its sometimes grating exuberance, the Yale University Art Gallery’s survey of its recent acquisitions gives the viewer a heightened appreciation for the diversity of art. After I finished my tour of “Art for Yale,” I was seized with a sudden urge to photograph the pigeon feathers, flies and white cigarette butts trampled into the cobblestones outside the gallery. There’s something unquestionably impressive about an exhibition so mind-expanding that it made me see art even in the Chapel Street sidewalk.