"Chaos is order yet undeciphered," reads the opening title card of "Enemy," Denis Villeneuve's (2013's "Prisoners") bravely imaginative, startlingly unnerving, freakily mesmerizing puzzle-box mindbender. A Freudian study of waking nightmares, hidden desires, and the despair of losing one's identity, the film—based on the novel "The Double" by Nobel Prize-winning author José Saramago—is the kind of infinitely layered cinematic miracle that deserves to be pored over, obsessed about and studied for years to come. As entrancing as the story is on its own, it's what is revealed the longer one watches and contemplates that transforms the picture into something altogether larger and more hauntingly evocative.

As college professor Adam Bell (Jake Gyllenhaal) teaches his class day after day about dictatorships and the universal drive for control—a pattern, he says, that repeats itself throughout history—he is unaware of the related cosmic forces at work in his everyday existence. Fastened into a dull daily routine, his relationship with girlfriend Mary (Mélanie Laurent) only coming alive long enough each night when he asserts himself in bed, Adam is looking to shake things up. His first attempt to do so is small but emphatic, renting a supposedly "cheery" movie called "Where There's a Will, There's a Way" based on the recommendation of a film-buff colleague. He doesn't think much of it at first, but a dream that night draws him back to the DVD still sitting in his laptop drive. Right there in the picture, Adam spots something he hadn't before: an actor playing the bit part of a bellhop who is his physical dead ringer. He researches the man, a struggling performer with the stage name Daniel Saint Claire, and learns that he, too, lives in Toronto. Adam cannot put his curiosity at bay until he gets to the bottom of this baffling situation, but once he takes that crucial step of meeting him in person, there may be no going back.

Existing on a fragile plane between uncanny reality and phantasmagoric horror, the smoggy Canadian cityscape which "Enemy" resides feels identifiable yet disquietingly off-center, at once modern and eerily post-apocalyptic. The same could be said for its four central characters—Adam, Anthony (Daniel's real name), Mary, and Anthony's pregnant wife, Helen (Sarah Gadon)—their fates careening simultaneously out of control and squarely toward their intended destinations. With composers Daniel Bensi and Saunder Jurriaans' (2011's "Martha Marcy May Marlene") propulsive score urgently bleeding into each successive scene, director Denis Villeneuve and screenwriter Javier Gullón fascinatingly delve into the psychology of a human being faced with the internal crisis of having a doppelgänger and the question of what makes him or anyone else unique. If Adam is taken aback by his life-altering discovery, his ensuing correspondences with Anthony and Helen create a ripple effect reverberating to their respective cores. Helen is confused but also intrigued, at one point following Adam to work to catch a glimpse of him for herself, while Anthony looks to eventually exert control over his new knowledge—a dangerous but inevitable reaction that harkens back to Adam's cautionary history-class lectures.

Jake Gyllenhaal's (2012's "End of Watch") exceptional performance portraying the dual Adam Bell and Anthony Claire is a master class in acting. Looking precisely the same as both men but steadfastly able to navigate between them without confusing the viewer in regard to which one is on the screen, he wholly embodies the quiet, introspective Adam, the more confident, commanding Anthony, and, without giving key developments away, other permutations of these two men and the roles they play. Witnessing Gyllenhaal's tremendous turn against the backdrop of director Denis Villeneuve's symbolic narrative labyrinth is simply too riveting to turn away from. As Mary, Mélanie Laurent (2013's "Now You See Me") brings her reliable alluring intelligence to a career woman trying to navigate her relationship with Adam while unknowingly becoming a pawn in his precarious association with Anthony. Finally, Sarah Gadon (2012's "Cosmopolis") emanates an ethereal yet determined quality as Helen, struggling to hold together her marriage—one that has been dishonest in the past—while also uncontrollably drawn to this stranger who has entered their lives.

The drive for power and the fear of losing oneself to interpersonal commitment, children and a clothesline of other mounting grown-up responsibilities are explored with shuddering, insatiable surrealism in "Enemy." In an early scene set at a fetish club, two strippers parade onto the stage surrounded by practically drooling men hanging on their every step. When one of them lifts the lid on a serving tray to reveal a tarantula, the initial threat of the animal's appearance is put into fuller perspective when the woman's stiletto heel lingers over the arachnid's creepy-crawly but intensely vulnerable body. This thematically stirring motif (inspired, Villeneuve has said, by Louise Bourgeouis' daunting sculptures) continues from start to finish; in another scene—not by accident proceeding Anthony's get-together with his overly critical mother (Isabella Rossellini)—a giant, spindly-legged spider is captured hovering over the high-rises of the city skyline, the very world in its clutches. The ending, as frighteningly perplexing on first viewing as it is ingeniously circular on later inspection, provokes and invigorates, capped by resounding, note-perfect musical accompaniment: "After the Lights Go Out" by The Walker Brothers. Backed with Matthew Hannam's quixotic editing and Nicolas Bolduc's visually somber, emotionally electric cinematography, the blazing technical components and fractured metaphors of "Enemy" merge into an ominously sublime whole. Indeed, the deeper Adam and Anthony dare to venture into one another's personal environments and plagued psyches, the more shrewdly sinister the film's imposing allusions become.