It’s amazing how far Coldplay has come in the past decade: At this time in 1998, they were a college-based band in London. By 2000, with the release of “Parachutes” and their hit “Yellow,” they got big. “A Rush of Blood to the Head” then made Coldplay both a critic and fan favorite, winning the Grammy for Best Alternative Album and selling over 12 million copies worldwide.

By 2005’s “X&Y,” the band was huge: It had released the world’s second best-selling album of 2005 and was the first British rock band to debut in the U.S. Top 10 since The Beatles. Nowadays, the band is so huge that even their shy bassist, Guy Berryman — worth over $25 million — is one of England’s richest people under 30.

But discontent has been growing among the Coldplay ranks for the past few years. The band’s popularity began to outpace their artistic growth, and after winning nearly universal praise for their earlier releases, “X&Y” fell flat with most critics. A New York Times reviewer famously labeled Coldplay “the most insufferable band of the decade.”

Cue the redemption album — the one designed to demonstrate that a band can be both hugely popular and artistically good. Coldplay’s result is “Viva La Vida,” released on June 17 in the U.S.

And for the most part, it’s a success. Swirling strings, exotic soundscapes and shifting song structures abound on the album, produced by living legend Brian Eno.

The first track, “Life in Technicolor,” is a shimmering, ambient instrumental, featuring the catchiest guitar line of the album. At the same time, however, the band’s decision to make an instrumental exemplifies Coldplay’s flawed new approach of avoiding their old ways at all costs.

The old Coldplay had developed a pretty strong formula: instrumental introduction; relatively sparse, even-keeled verse; and huge, catchy, stadium-rocking chorus. Of course, repeated for good measure. It worked on everything from “Yellow” to “In My Place” to “Clocks” to “Speed of Sound.” But now they deliberately avoid this easy route. Chris Martin and company break up single tracks into multiple parts on “Viva La Vida,” and at times, this works. But other times, Coldplay fails to develop the parts that actually work best.

For example, the third track, “42,” has three unrelated parts that stand up well individually: a piano melody, a “Paranoid Android”-like guitar breakdown and finally a rousing refrain. Although each part is good on its own, they don’t necessarily work to make each other better.

“Yes” is another example. The song starts off with swirling Middle Eastern strings, pauses and then launches into a shoe-gaze song. The individual parts are well done, but squashing them together doesn’t add much.

The songs that the band does keep fully intact stand up best. “Viva La Vida” is a string-drenched anthem that recently topped the American music charts. Sung from the perspective of a king deposed by revolution, it features Chris Martin’s most interesting lyrics to date. “Violet Hill,” the first single from the album, sports a distorted riff and political lyrics. “Lost!” is driven along by a processed drum beat and handclaps layered with wide-screen church organ.

In the end, “Viva La Vida” manages to expand Coldplay’s musical repertoire by small measures, but doesn’t fundamentally alter the band’s sound (a win-win situation for fans): The hooks are still catchy. The beautiful textures are still there. Martin’s emotions are still on his sleeve. But now the old formula is pretty much gone, and Coldplay is out of its rut — their brand bigger and better than ever.