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In September 2006, an 18-year-old English girl who had just graduated from high school named Adele Adkins signed a deal with XL, a prominent independent label that had released albums by such artists as the White Stripes, M.I.A. and Radiohead’s Thom Yorke. The London-based imprint had been run by record producer Richard Russell since the mid-’90s, and under his direction it became known for putting out a wide variety of music in many genres, often—but not always—with a focus on electronic music. More than being known for any single genre, XL is prized for its taste and unwavering sense of cool. Adele’s debut album, “19,” assembled when she was the titular age, was like a trip through a well-curated record collection, touching folk, jazz, R&B and pop, all of it anchored by her once-in-a-generation voice.

In the years since, Adele, who has since signed with Columbia, a major label, and became one of the biggest stars in music and is by some measures the bestselling artist of this century. While her music has cross-generational appeal and has scored big on the adult contemporary charts as well as the Hot 100, she’s never lost touch with the impeccable aesthetic sense she had early on. Her influences come from across the decades—American R&B artists such as Mary J. Blige and Aaliyah, cocky millennial pop stars like Lily Allen, and blues and jazz singers including Ella Fitzgerald and Etta James —and she has a real skill for transporting the gravitas of music’s past to the sound and style of its present.

Her fourth album, “30” (Columbia), out Friday, finds Adele achieving a rare balance among competing forces, including between experimentation and accessibility. The immense lead-up to the album’s release—early single “Easy on Me” set streaming records and topped many charts, and her television special, “Adele One Night Only,” which interspersed performance footage with interviews with Oprah Winfrey, had television ratings that almost matched this year’s Academy Awards—positioned “30” as her divorce album, written and recorded as her relationship with entrepreneur Simon Konecki was crumbling. Given her towering celebrity profile and the stakes involved with the release of a new LP, it is tempting to think of “30” as an expression of her cult of personality, a blockbuster entertainment that is merely the latest iteration of a successful franchise. But the album resists such neat classification. It’s a more daring record than 2015’s “25,” both emotionally and formally, and Adele has an uncanny ability to transform her own struggles into music that seems like it’s about yours.

The tracks here come from a familiar array of collaborators—co-writers and producers including Greg Kurstin, Tobias Jesso Jr. and Max Martin all contributed to her previous album—but Adele bends their styles to fit her own, and the record feels like a unified statement. A viewing of the 2019 Judy Garland biopic inspired the opening “Strangers by Nature,” Adele said in a recent Rolling Stone interview, and the song introduces impressionistic string orchestrations that crop up through the record. She sings it like a 1950s standard, with a vibrato-heavy inflection that brings to mind the torch songs of Billie Eilish’s recent album, and it’s a moment of levity on a record that veers toward darkness. “I’ve never seen the sky this color before,” she sings, conveying the thrill of a new love. “It’s like I’m noticing everything a little bit more.”

The lyrics throughout “30” are steeped in language that draws from contemporary notions of self-care and feature the self-reflection common in therapy, but Adele has good instincts for when to pull back before a song gets too self-involved. The second track and lead single, “Easy on Me,” is in the vein of earlier mega-hits like “Someone Like You” and “Hello,” but it feels more relaxed and lived-in than its predecessors, radiating wisdom and clarity without sacrificing the singer’s astonishing vocal power.

The following track, the strange and haunting “My Little Love,” is the record’s riskiest turn. Over a backdrop of ghostly vocals and eerie strings, Adele sings to her son, who struggles to understand his parents’ separation. “I know you feel lost, it’s my fault completely” is one of many gut-wrenching lines, and the song ratchets up the angst with interludes that feature scratchy recordings of Adele conversing with her child about the situation. For some, this song will tip over into creepy voyeurism, and there are ethical questions about including on a record such an intimate exchange with a boy so young. But the cumulative effect of the melody, the words and the shadowy beauty of the production is completely overwhelming.

Smartly, Adele follows that devastating song with the album’s best pop track, the gospel-inflected “Cry Your Heart Out.” Its shuffling beat brings to mind classic Motown, and the pitched-up background vocals by Adele call back to the soul-sampling hip-hop pioneered by Kanye West in the early 2000s. This soulful vibe continues on “Oh My God,” and then “Can I Get It,” written with and produced by Mr. Martin and his partner Shellback, is a snapping pop number driven by acoustic guitar that sounds like a future hit. This terrific up-tempo run is interrupted with the lengthy self-examining ballad “I Drink Wine” and then the curious “All Night Parking,” which finds Adele singing over a crackly sample of cocktail-jazz piano trills by Errol Garner.

For those first two-thirds, “30” is fantastic and often stunning, but the album’s final four songs, all of which are at least five minutes long and two of which almost reach seven, can’t quite sustain the quality. “Woman Like Me” has an intriguing atmosphere with a folky acoustic guitar and Adele’s voice dripping with reverb, but the melody is vague. “Hold On” takes advantage of that space to move from an ultra-spare ballad with just piano and voice to a grand sing-along, but “To Be Loved” stretches on with no real payoff. The closing “Love Is a Game” is better, returning the album to where it started, with a lovely string arrangement and a cinematic mood. Adele seems to grapple with the gap between her creative life, where she has ultimate control and has found almost unbelievable success, and the more difficult everyday world of love and family: “How unbelievable of me to fall / For the lies that I tell, the dream that I sell.” Wherever she lands in her own life during this time of tumult, her artistic instincts are as sharp as ever, and “30” is superb.

—Mr. Richardson is the Journal’s rock and pop music critic. Follow him on Twitter @MarkRichardson.