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Making its Muny debut this week, “Young Frankenstein” is a Mel Brooks show. That says it all.

It’s packed with jokes sophisticated and silly (by Brooks, who wrote the book with Thomas Meehan), clever songs (words and music by Brooks), a dash of naughty humor (signature Brooks), and references to movies of an earlier era (which Brooks apparently memorized).

In fact — and this should come as no surprise — it’s based on, and closely follows, his 1974 movie of the same name, a hilarious take on old horror pictures.

In the last few seasons, the Muny has had a lot of success with splashy musical comedies like this one, such as “The Producers” (also Brooks), “Spamalot” and “The Addams Family.” Loose-limbed and goofy, they take over the roomy stage like kids on a playground. Save the golden-age ballads for another day.

Marcia Milgrom Dodge, who directed the “The Addams Family’s” Muny debut two years ago (as well as last summer’s hit “Buddy: The Buddy Holly Story”), knows just what to do with this kind of material. She keeps the jokes coming fast and the numbers big and bright. That’s this kind of entertainment.

Robert Petkoff stars as Frederick Frankenstein, a brilliant New York doctor. But he must return to his family’s home in Transylvania to claim his estate or lose it. The townspeople still remember his grandfather, a mad genius who terrified them with his experiments. Surely Young Frankenstein wouldn’t do the same thing ... or would he?

Dolled up in a wild wig that evokes Gene Wilder (who starred in the movie), Petkoff gives the show its wiggly center. He’s supported by a terrific cast of character actors, including Steve Rosen as the doctor’s weird assistant Igor, Stephanie Gibson as his gorgeous assistant Inga and John Scherer as a well-intentioned but inept blind hermit.

Vicki Lewis is just perfect as the stern housekeeper, Frau Blucher, especially when she sings her mordant song of doomed love, “He Vas My Boyfriend,” in the style of Marlene Dietrich. (Or maybe it’s in the style of Madeline Kahn, who performed a very similar number in another Brooks opus, “Blazing Saddles.”)

But maybe the real star of this show is the choreographer, Josh Rhodes. His wide-ranging talents take us from a parody of colorful peasant dances (“The Happiest Town”) to a spoof of old dance crazes (“Transylvania Mania”) to a brilliant number for Jennifer Cody and the ensemble.

Cody plays the doctor’s fiancée, a pampered heiress who’s strictly off-limits. For her anthem, “Please Don’t Touch Me,” Rhodes creates a romantic duet that takes the title literally. It’s comedy choreography in a class all its own.

And then there’s his masterpiece, his tap-spectacular treatment of Irving Berlin’s “Puttin’ on the Ritz.”

It starts out as a dance for the doctor and his green-faced Monster, played with considerable elan by Timothy Hughes. With their tuxedos and walking sticks, they make a debonair duo.

But then Hughes continues to dance, first in a classic mirror number with some members of the ensemble and then with all of them, including deftly tapping children. All dressed like Hughes, they provide an irresistible beat while music director Charlie Alterman and the orchestra soar on the jazzy melody (the only song in the show that Brooks didn’t write). It’s a total high.

Compared to a lot of today’s entertainment, “Young Frankenstein” seems pretty tame. Still, it has its share of “What does that mean, Mommy?” jokes, so it may not be for everyone. But fans of Brooks can probably fill the Muny all by themselves.

“Young Frankenstein”

When • 8:15 nightly through July 19

Where • The Muny, 1 Theatre Drive, Forest Park

How much • $14-$90, plus the free seats

More info • 314-361-1900; 314-534-1111; muny.org

Judith Newmark is the theater critic for the St. Louis Post-Dispatch.