There is something innocent about Garry Marshall when he talks about Happy Days, the 1950s teen-based sitcom he created exactly 40 years ago.

This is fitting somehow for a writer, director and producer who came of age in a post-Second World War era of rock'n'roll and high-school hops he mythologised on a show that became a key part of a nostalgia boom that has never really gone away.

Initially piloted as a one-off episode of Love, American Style, Happy Days ran for 255 episodes between 1974 and 1985. The show's initial focus on Ron Howard's straight-laced good guy Ritchie Cunningham was soon upstaged by Henry Winkler's leather-jacketed cool guy Arthur The Fonz Fonzarelli, who stole the show enough to become a household name.

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Almost 30 years after the TV show ended, Happy Days: A New Musical has opened in Glasgow as part of its UK tour in a production written by Marshall alongside Bugsy Malone composer Paul Williams.

Set around the time of Series 4 of the TV series, Happy Days: A New Musical (which stars Ben Freeman, ex Bucks Fizz singer Cheryl Baker and former Sugababe Heidi Range) focuses on Richie, Fonzie and the gang's attempts to save their regular hang-out, Arnold's malt shop, from a construction company's plans to turn it into a shopping mall.

This in itself speaks volumes about how much Marshall's creative heart still resides in a small-town America unspoilt by the sort of commercialised landscapes that are now taken for granted in more recent teen-based television. It is this depiction of a simpler life too that Marshall sees as crucial to Happy Days' enduring appeal.

"Who would have thought we would still be talking about it 40 years later?" says the 79-year-old. "But people seem to like nostalgia. Happy Days was always very positive. It is certainly not a reality show, but it was based on a lot of stuff. I grew up not too rich in the Bronx, and I was sick all the time, so I dreamt up a lot of stuff.

"The original request was to do something nostalgic that was set in the 1930s, but I grew up in the 1950s, when there were nice days, no drugs and everything was kind of calm. How to make calm exciting was my job, but the first pilot for the show didn't sell. They said, 'Who needs the 1950s?' but then a wonderful film came out called American Graffiti, and everything changed."

American Graffiti was future Star Wars director George Lucas's 1973 film about a group of teenagers coming of age in the early 1960s. Crucially, one of the cast was Ron Howard, who would go on to play Richie in Happy Days. A year later, Henry Winkler appeared in The Lords Of Flatbush, a low-budget feature based on a group of teenagers in 1950s Brooklyn.

If Winkler's performance could be viewed as a harder-edged dry run for Happy Days, then a template for Happy Days' more saccharine approach had already been set by Grease, Warren Casey and Jim Jacobs's 1971 musical, which would go on to mirror the success of Happy Days in its 1978 film version starring John Travolta and Olivia Newton John.

For Marshall, the son of a tap dance teacher and an industrial film director whose career began as a joke-writer for assorted comedians before going on to script The Dick Van Dyke Show, The Lucy Show and a TV version of Neil Simon's The Odd Couple, Happy Days was to lead to a big screen career of his own. He would go on to direct Pretty Woman, Frankie And Johnny, Runaway Bride and The Princess Diaries.

Happy Days: A New Musical appeared in 2007, although it had been in development for much longer. "There were a lot of challenges," Marshall says, "and we had to keep doing it until we got it right. I have a theatre in Burbank, Los Angeles, so we work-shopped it there. I had different companies telling me different things, but I wanted the storyline to stay true to the spirit of the series."

Beyond the stage musical, the legacy of Happy Days has left its considerable mark on the film and TV world, with the programme spawning no less than eight spin-off shows, including Laverne & Shirley, which featured Marshall's sister Penny, and Mork And Mindy, which made the then unknown Robin Williams a star.

Happy Days is also notable for many of its cast going on to be directors. Ron Howard left the show in 1980 to concentrate on a career that has seen him direct more than 30 features, including Frost/Nixon, How The Grinch Stole Christmas, Apollo 13 and Splash. As a producer Howard has also made his mark and most recently was executive producer of TV drama Arrested Development.

Anson Williams, who played Potsie Webber in Happy Days, has directed a stream of TV shows, including Beverley Hills 90210, Sabrina The Teenage Witch and Charmed. Given the nature of much of both men's work, it is clear who their inspiration was.

"I learned in showbusiness you have gotta do everything," says Marshall. "Happy Days was a phenomenon that changed my life, and enabled me to do other things, so I would encourage everyone on the show to do the same. Five directors came out of that show, and Ron Howard went on to become one of the best film directors around."

After the Happy Days musical began in London, he was planning to see Stephen Ward, Andrew Lloyd Webber's 1960s-set musical about the Profumo scandal that presents an altogether more salacious image of the period that directly follows the Happy Days era.

"Now it would have to be done edgier, darker, more risque," Marshall says of his TV show. "In the series, they would not even let us use the word 'virgin', but we did our own issues. Richie had a motorcycle accident where if he had not been wearing a helmet he would have died. In the end, if a show is done well, then it works, and it doesn't matter if its edgy or innocent."

Looking ahead, Marshall has a desire to do a new show. "I don't know if I will ever get something as good as Happy Days," he says, "but you gotta keep trying."

Happy Days: A New Musical is at King's Theatre, Glasgow until March 1; His Majesty's Theatre, Aberdeen, May 5-10; King's Theatre, Edinburgh, May 12-17.