J.K. Rowling, author of the Harry Potter series of books, has had a meteoric rise from obscurity into the ranks of the world’s richest women by imagining things and people that don’t exist and drawing connections to the real world. Her fiction delivers calm and specific messages about injustice, social caste systems, racial prejudices and the sense that people in power are capable of dire actions.

Rowling has created not only the most-read children’s literature to date, teaching them about good and evil, but has won remarkable adult success as well. It is exceptionally timely work, a cultural phenomenon that moves ahead true to its roots in the well-told and action-packed adaptation of “Fantastic Beasts and Where to Find Them.”

It is clearly shaped by the present international rise of xenophobia, and handles its topical themes with care. It is also a thoroughly satisfying, wildly entertaining and highly enjoyable ride from the very beginning to the very end.

A lavish prequel to her Potter series, this entry is based on an original script by Rowling rather than an adapted novel. It’s set in a vibrant rendering of 1926 New York City, a glittering metropolis with a dismal underbelly. Director David Yates, who made the final four films in the Potter series, knows precisely what his audience wants, crafts it with immaculate precision and delivers it in double scoops. With uncanny set design, costuming and lavish cinematography, he creates an old-time backdrop with a perfect balance of the familiar and the weird, one of the finest examples of period world-building I have seen.

At the center of the action is Newt Scamander, who was only passingly mentioned in Rowling’s earlier novels, a wizardly zoologist researching magical creatures on a worldwide expedition. He steps off the transatlantic boat to connect with the big city’s resident witches while attending the Magical Congress of the United States of America. What he encounters is far from the golden door promised by the Statue of Liberty.

After a building-crumbling wave of magical destruction that endangered human life, the city’s enchanters have gone into hiding. Angry citizens who feel vulnerable call for the return of Puritan witch trials. It’s the sort of movement that springs up in an atmosphere of fear, suspicion and economic hardship, all of which the film portrays with an aura of foreboding.

The central mystery is who or what caused the demolition attacks, and why. Whether it’s criminal activity or a blowback from forces being demonized by oppressors are questions that Rowling’s carefully controlled screenplay gives a well-defined arc. Master storyteller that she is, she also gives her cast doses of uplifting comedy.

Eddie Redmayne is a calm, soft-spoken, sometimes blundering delight as the animal specialist, whose suitcase is filled with magical animals that tend to escape and run wild at the worst times. He’s amusing just standing still, wearing a half-combed thatch of Absent-Minded Professor bangs and looking at his fetching female co-stars with a shy, No Romance Please, I’m British smile. In a par excellent performance, he easily ranges from sequences where he is thoroughly restrained to moments of pure hilarity. Trying to control a huge creature by copying its mating dance, he shimmies a jig that must be seen to be believed.

The entire cast is wisely chosen, each chipping in a tone all their own. As half of the central quartet, Katherine Waterston and Alison Sudol play wildly differing magical sisters, a no-nonsense law enforcement officer and an all-heart free spirit with a voracious attitude for mind reading. Sudol is outstanding in a comic love story with Dan Fogler, delivering great Brooklyn vernacular as an everyday schmo pulled off the streets and into the wizarding world for the whole wild toboggan ride. Colin Farrell is legitimately creepy as the wizards’ equivalent of an FBI chief, part detective, part the good characters’ nemesis. And if you don’t know it (and I hope you don’t), a major screen star appears in a surprise cameo likely to prove crucial in sequels to come.

This is a truly magical experience in every sense of the word. This is not only a good film — quite possibly the best chapter of its series since 2004’s “Harry Potter and the Prisoner of Azkaban” — but in a strange way, it is an important one. It shows how pluck and perseverance and goodwill — and, frankly, a magic wand — can stand up to unsettling challenges. One hundred percent recommended. Multiple viewings advised.