“No war! No war!” chants Bono at the conclusion of “Sunday Bloody Sunday” as a fan tosses the Irish flag onstage. It is an eerily familiar sight for anyone who recalls the quartet’s mid-’80s gigs in which the singer would attempt to solve the problems of world famine, social injustice and inner-city traffic congestion all before the second encore.

Certainly anyone returning to U2’s orbit at this moment in time after a decade-and-a-half’s absence might conclude that the band has spent the intervening years simply rehashing the same musical shapes and heartfelt sloganeering, with only Bono’s now mercifully mullet-free head deferring to any change in fashion.

Of course, as history records, the foursome’s trio of ’90s albums (Achtung Baby, Zooropa and Pop) saw them not treading water but departing from rock’s heated pool of well-meaning worthiness altogether, as they traded pain, guitars and degree-level geopolitics for pleasure, synthesizers and Las Vegas.

But the band’s latest album, All That You Can’t Leave Behind, finds them reverting to less frivolous ways, including, as it does, paeans to political martyrs and dead friends. Moreover, prior to the start of this spring-summer Elevation tour, Bono had said “this [show] is about making rock music big again,” and tonight it seems clear that U2 are serious about getting serious.

Bono dedicates “The Sweetest Thing” — which finds him playing rudimentary piano — to his pregnant wife, Ali, and “Stuck in a Moment You Can’t Get Out Of” to late INXS singer Michael Hutchence. Most songs are rendered faithfully, except for a spare — and improved — voice-and-acoustic-guitar “Angel of Harlem.”

Revisiting each of their last eight albums (except, notably, Zooropa), the band also seems keen to point up what connects their more recent work with earlier endeavors rather than what separates it. In particular, U2 return again and again to the same lyrical themes — unity, faith, the limits of strength, transcendence — regardless of whether they happen to be finding musical inspiration from B.B. King or mid-period Bowie.

Another link with the past can be found in Bono’s longstanding magpie-like tendencies. “Every artist is a cannibal/Every poet is a thief,” he sings on “The Fly,” and you have to admire both his sharp teeth and quick fingers. “Stuck in a Moment” is such a blatant rewrite of Curtis Mayfield’s “People Get Ready” — a song U2 covered often on their 1987 tour — it almost counts as sampling.

Bono, as always, also slips choruses of other people’s songs into his own, touching on Radiohead’s “Creep” in “Elevation,” Van Morrison’s “Crazy Love” in “In a Little While” and not one but two Bob Marley songs in “Sunday Bloody Sunday.” Hutchence, meanwhile, receives another nod as the frontman takes a detour through INXS’s “Devil Inside” in the course of a bristling “Discothèque.” Finally, there is no doubt that much of the new material, such as the eco-disaster–oriented “Beautiful Day,” has far more in common with “Bad” and “Sunday Bloody Sunday” — both of which receive an airing — than anything on Achtung Baby or Pop.

Yet despite the impression that U2 have come to reclaim their position as a no-nonsense, old-school stadium rock act, it’s clear that their decade of experimentation has left its mark on tonight’s show.

The stage set, which resembles nothing so much as the lobby of a chic urban hotel, may pale in comparison to the Zoo TV and Popmart kilowatt extravaganzas but still features four overhead screens plus another 13 televisions behind the drum kit — all of which is in dramatic contrast to their frippery-free pre-Achtung days. Bono has also learned that sometimes the best thing to do with your tongue is to keep it in your cheek, finding time to make fun of bassist Adam Clayton’s “just-back-from-Pakistan look” and introducing the Edge as “the scientist of the band.” It is an approach that is lapped up by the fans, nearly all of whom remain standing throughout the two-hour show.

Best of all, U2’s decision to scale back from stadiums to arenas means that it is possible to examine and enjoy all this from the same ZIP code as the band. Or even from onstage, as one dark-haired minx successfully attempts, to be rewarded with a slow dance from Bono as he croons Marvin Gaye’s “Sexual Healing.” The result is a superb fusion of new and old, large-scale and intimate, which once again justifies Bono’s 20-year-old declaration — made when they were still playing to crowds of fewer than 100 — that U2 were “meant to be one of the great groups.”