“I think of women’s fitness history as B.J. and A.J. — Before Jane and After Jane,” Ken Alan, a kinesiologist who taught aerobics in the 1970s, said in a 2020 interview.

Ms. Fonda initially entered the exercise business to raise money for her husband, the progressive activist Tom Hayden, who had dreams of running for local office. In 1979, she opened her first studio, Jane Fonda’s Workout Studio in Beverly Hills. Its exercise classes — taught to Top 40 hits and sometimes led by Ms. Fonda herself — were packed with locals, tourists and the occasional A-list celebrity. Her signature class was a cardio and resistance routine set to the Jacksons or REO Speedwagon that worked all the major muscle groups.

The studio’s success soon led to “Jane Fonda’s Workout Book” in 1981, which sold two million hardcover copies, hit the top of the New York Times best-seller list and prompted the biggest royalty check Simon & Schuster had ever signed.

Thanks largely to Ms. Fonda’s influence, America’s obsession with Lycra, leotards and getting fit transcended the gym and seeped into pop culture. That same year, Olivia Newton John released “Physical,” an ode to exercise that became the country’s number one single.

But the real revolution was still to come. In May 1982, Ms. Fonda released the “Jane Fonda Workout” on a still-niche VHS tape, featuring her signature workout routine.

In its first three years, the tape sold 850,000 copies — more than “Alien” or “Jaws” — and became the best-selling home video up to that point, despite costing $59.95 (the equivalent of $190 today).

Some credit the video with helping to launch the entire VHS industry. In 1980, about two and a half percent of households owned a VCR; by 1985, about a third did. Ms. Fonda would eventually release 22 workout videos, collectively selling more than 17 million copies.

The workout fads of the ’70s and early ’80s created a new ideal of beauty for both men and women and cemented the idea that exercise was fundamental to healthy living. Magazines, films and TV shows began featuring more muscled (though still thin) physiques. By the end of 1982, Ms. Fonda — standing on the toned shoulders of early joggers, Jazzercisers, yogis and weight lifters — had ushered in the fitness culture we know today.

More than 40 years later, when we sign up for a road race or go to a CrossFit gym, lift a kettlebell or do a downward dog, we are still sweating in the world they built.