Eddie Van Halen, whose razzle-dazzle guitar-playing — combining complex harmonics, innovative fingerings and ingenious devices he patented for his instrument — made him the most influential guitarist of his generation and his band, Van Halen, one of the most popular rock acts of all time, died on Tuesday. He was 65.

Mr. Van Halen’s son, Wolfgang, said in a statement that his father had “lost his long and arduous battle with cancer.” The statement did not say where he died.

Mr. Van Halen structured his solos the way Macy’s choreographs its Independence Day fireworks shows: shooting off rockets of sound that seemed to explode in a shower of light and color. His outpouring of riffs, runs and solos was hyperactive and athletic, joyous and wry, making deeper or darker emotions feel irrelevant.

“Eddie put the smile back in rock guitar at a time when it was all getting a bit broody,” his fellow guitar ace Joe Satriani told Billboard magazine in 2015. “He also scared the hell out of a million guitarists because he was so damn good.”

Mr. Van Halen was most widely revered by his peers for perfecting the technique of two-handed tapping on the guitar neck. That approach allowed him to add new textures, and percussive possibilities, to his instrument, while also making its six strings sound as expressive as a piano’s 88 keys or as changeable as a synthesizer. He received patents for three guitar devices he had created. In 2012, Guitar World Magazine ranked him No. 1 on its list of the “100 Greatest Guitarists of All Time.”

“I’m always pushing things past where they’re supposed to be,” Mr. Van Halen told the educational website Zocalo Public Square in 2015. “When ‘Spinal Tap’ was going to 11, I was going to 15,” he said — a reference to that film’s famous joke about a guitarist who dubiously claims that his amplifier can exceed its highest decibel level.

The zest in Mr. Van Halen’s playing paired perfectly with the hedonistic songs and persona of his hard-rocking band, Van Halen, whose original lineup featured his brother Alex on pummeling drums, Michael Anthony on thunderous bass and the singer David Lee Roth, who presented a scene-stealing mix of Lothario, peacock and clown.

Formed in 1972, Van Halen went on to sell more than 56 million albums in the United States alone. Ten of the band’s studio albums (some of which were cut with Sammy Hagar as lead singer during a long split with Mr. Roth) went multiplatinum. One sold more than six million copies (“5150” in 1986, featuring Mr. Hagar); another sold five million (“Van Halen II” in 1979); and two passed the 10 million mark to achieve “diamond” status (the band’s debut, “Van Halen,” in 1978, and “1984,” issued the year in the title).

Eleven of the band’s studio albums reached the Top Five, and four snagged the top spot on Billboard’s Top 200. Van Halen amassed eight Billboard Top 20 singles, including its cover of Roy Orbison’s “(Oh) Pretty Woman,” which reached No. 12 in 1982, and “Jump,” which seized the No. 1 spot in 1984 and held it for five weeks. In 2007, the band — including both Mr. Roth and Mr. Hagar — was inducted into the Rock & Roll Hall of Fame.

Edward Lodewijk Van Halen was born on Jan. 26, 1955, in Amsterdam to Jan and Eugenia (Beers) Van Halen. His father, a struggling Dutch classical musician who played clarinet, saxophone and piano, met his Indonesian-born wife while on tour in Indonesia.

In 1962, when Mr. Van Halen was 7, his family relocated to the United States, driven away by prejudice against his mother and unfavorable work opportunities in the Netherlands. They settled in Pasadena, Calif. His mother worked as a maid, his father as a janitor while seeking work as a musician.

In a new country, with a new language to learn, the Van Halen sons, Eddie and his older brother, Alex, turned to music as their lingua franca. Eddie first studied classical piano, which he excelled at despite a serious limitation.

“I never learned how to read music,” he told Rolling Stone in 1995. “I fooled my teacher for six years. He never knew. I’d watch his fingers, and I’d play it.”

Inspired by the British group the Dave Clark Five, Mr. Van Halen and his brother began playing rock ’n’ roll, with Eddie on drums and Alex on guitar. They switched instruments once Eddie discovered that his brother had a better feel for percussion.

The siblings formed their first band in 1964, the Broken Combs, which became the Trojan Rubber Company. In 1972 they formed a new group, calling themselves Genesis, even though there was already a British band by that name. They rented a sound system from Mr. Roth, whom they eventually hired as their singer — but only, Mr. Van Halen later said, to save the rental money. Two years later, they recruited Michael Anthony on bass and changed their name first to Mammoth and then to Van Halen.

The foursome developed a loyal following at clubs in Pasadena and Hollywood and were introduced to Gene Simmons of Kiss. Impressed by their cockiness as well as their talent, he produced their first demo and took it to his band’s manager to sign them — to no avail.