“Take Dada seriously — it’s worth it!” said the artist George Grosz. The quotation is painted on the wall of one of the rooms in the Yale University Art Gallery’s newest exhibit, “Everything is Dada,” except it’s backwards — only when you see it reflected in a funhouse mirror do the words become intelligible.

Try to take Dada seriously and Dada will play a trick on you. Dada is naughty and elusive, the mischief-maker of the modern avant-garde, flicking the back of your head, whispering gibberish in your ear and scampering off before you’ve had the chance to catch him in the act. Dada is anti-capitalist and anti-establishment, it is absurd, it is moralizing, it is amoral. The playfulness of the YUAG’s exhibit complements this irreverent, all-encompassing and oftentimes mystifying movement.

The most widely recognized Dada artwork is Marcel Duchamp’s “Fountain,” which is just a urinal turned upside down. But the YUAG’s new exhibit, which opens today and runs until July 3, shows that Dada is much more than that, encompassing painting, sculpture, film and printmaking.

The curator of the exhibit, Frauke Josenhans, has drawn on the exceptional holdings of the YUAG to put on a diverse and representative show. “There aren’t that many museums that can do an entire Dada exhibit using only their own collections,” she said, citing MOMA and the Centre Pompidou as comparable institutions. Most of the collection is drawn from the gallery’s rich Société Anonyme collection, collected by Man Ray, Marcel Duchamp and Katherine Dreier and donated to Yale in 1941.

The selection is organized thematically. (For example, there’s a room called “Sense and Nonsense.”) The show’s curators have avoided a chronological or geographical approach to the movement, as this has been done many times before, and would perhaps fetter the wild beast that is Dada.

The curators have made some inclusions that might not be found in your run-of-the-mill Dada exhibit. Angelika Hoerle, Beatrice Wood, Suzanne Duchamp and Sophie Taeuber-Arp all have prominent roles in the exhibit, which emphasizes the often-overlooked role of female artists within the transnational movement. A room devoted to Dada film highlights the significance of that medium, which was central to the work of the Dadaists and their successors, the Surrealists.

The space itself reflects the movement’s ethos, or lack thereof: A perforated red-and-blue line zigs and zags across the sleek, whitewashed walls of the exhibit. The artworks, too, are staggered rather than aligned, sometimes moving up with the line and other times parting ways with it. The whole effect distances the viewer from the normal routines of museum-going: staring at one picture, inching to the right, staring at another picture, inching to the right.

The exhibit has more tricks up its sleeve. Red velvet curtains seem to promise an entire new room, but when you go in, you find yourself a foot from the wall, staring at a series of intimate watercolors by Beatrice Wood. In another room, designed by Yale MFA students, wild typographic patterns form and deform themselves on the walls, which are in turn covered with reproductions of artworks featured in the show. Neon lights flash at you; a pennant depicting Duchamp’s famous urinal hangs six feet above the ground. The room is stocked with fake Dadaist newspapers with headlines such as “First Dadaist Political Party from North Carolina” and “Are You Ready for a Disaster,” designed by Yale MFA students, which will be replenished while the exhibit runs.

Tristan Tzara began his famous Dada Manifesto of March 1918 by declaring: “The magic of a word — Dada — which has brought journalists to the gates of a world unforeseen, is of no importance to us.” He’s being coy, but he has a point: There’s no use defining Dada, because everything is Dada. And Dada (and everything) is of no importance. You’ll find yourself thinking in circles and riddles such as these as you walk the not-so-hallowed halls of “Everything is Dada,” which defies expectations, as the artists and thinkers it represents once did.