Ireland’s U2 is the most important and influential band of the post-punk era, joining ringing guitar rock, punkish independence, Celtic spirituality, innovative production techniques and electronic experimentalism all held together by singer/lyricist Bono’s transcendent vision and charisma. U2 Bono (Paul Hewson), guitarist the Edge (Dave Evans), bassist Adam Clayton and drummer Larry Mullen formed in Dublin in 1976 as a Beatles and Stones cover band while the players were all still in high school. In 1980 they were signed to Island Records and released their spectacular first album, “Boy,” produced by Steve Lillywhite.

Mike Hutchings / Reuters file U2, with guitarist the Edge and lead singer Bono, is now a mature, confident, still amazing band that knows it doesn’t have all the answers, but isn’t afraid to keep asking the right questions.

The band’s sparkling, radiant sound jumped from the grooves from the first note of “I Will Follow” and rode Mullen’s massive drums and the Edge’s angular, careening guitar into history.

Neither “Boy” nor its follow-up “October” (with the glorious “Gloria”) tore up the charts at the time (though both are now platinum), but “War” — passionate, martial “Sunday Bloody Sunday,” melodic wailing “New Year’s Day,” and the fierce, new wavy love song “Two Hearts Beat As One”—turned U2 into a worldwide phenomenon in 1983.

In preparation for 1984’s “The Unforgettable Fire,” producer Brian Eno had a long conversation with Bono, as he later told Q Magazine. “I said, ‘Look, if I work with you, I will want to change lots of things you do, because I’m not interested in records as a document of a rock band playing on stage, I’m more interested in painting pictures. I want to create a landscape within which this music happens.’ And Bono said, ‘Exactly, that’s what we want too.’”

The results of this fateful change of direction were Eno productions of U2 standards “The Unforgettable Fire” (including “Bad,” “Pride In the Name of Love”); Grammy’s 1987 Album of the Year, the personal yet universal “The Joshua Tree,” which made the band superstars (with “Where the Streets Have No Name,” “I Still Haven’t Found What I’m Looking For,” “With Or Without You” and “One Tree Hill”); 1991's “Achtung Baby,” a brilliant and emotionally dark move toward electronica (“Even Better Than the Real Thing,” “One,” “Until the End of the World,” “Who’s Gonna Ride Your Wild Horses” and “Mysterious Ways”); and “Zooropa,” deeper still into Euro-dance music and electronics (‘93, with the title track, “Numb,” “Lemon,” “Stay”). Wow, what a journey.

U2 was the leading rock band of the '80s because its members, like perhaps only Bruce Springsteen in the U.S., still believed that rock ‘n’ roll could save the world, and they had the talent to make that notion not seem hopelessly naive.

This earnestness and willingness to shoulder the heaviest of responsibilities led to soaring heights of achievement and escalating psychic and artistic demands that eventually led the band to adopt irony as its basic means of expression for a time in the '90s.

All bands want to be cool, and in the '80s U2 almost single-handedly made earnestness cool, but it was hard, relentless work. After the gritty, chunky guitars-and-idealism of the '80s, the '90s saw the diaphanous chill of electronics-and-irony, which was literally and metaphorically cool, but ultimately not what the band is about.

“All That You Can’t Leave Behind” (‘00) returned to what the band is about, and is the sonic and spiritual follow up to the “The Joshua Tree,” the band’s most idealistic, spiritual and melodically consistent album.

Remnants of the band’s forays into electronics seasoned the album (especially the impressionistic “New York”), but the Edge’s guitar returned to center stage where his unique, chiming style belongs, though it never upstages the songs, every one of which is blessed with a memorable tune.

Following the ecstatic release of the opening track “Beautiful Day,” the second song “Stuck In a Moment You Can’t Get Out Of,” states a seemingly modest but deeply profound, earnest and idealistic notion:

“I’m just trying to find a decent melody A song I can sing in my own company”

They have found it and then some. U2 is now a mature, confident, still amazing band that knows it doesn’t have all the answers, but isn’t afraid to keep asking the right questions.