If movies are shared dreams, then Christopher Nolan is surely one of Hollywood’s most inventive dreamers, given the evidence of his commandingly clever “Inception.” Applying a vivid sense of procedural detail to a fiendishly intricate yarn set in the labyrinth of the subconscious, the writer-director has devised a heist thriller for surrealists, a Jungian’s “Rififi,” that challenges viewers to sift through multiple layers of (un)reality. As such, it’s a conceptual tour de force unlikely to rank with Batman at the B.O., though post-”Dark Knight” anticipation and Leonardo DiCaprio should still position it as one of the summer’s hottest, classiest tickets.

Our guide to this world of high-stakes corporate espionage is Dom Cobb (DiCaprio), an “extractor” paid to invade the dreams of various titans of industry and steal their top-secret ideas. Cobb plunders the psyche with practiced skill, though he’s increasingly haunted by the memory of his late wife, Mal (Marion Cotillard), who has a nasty habit of showing up in his subconscious and wreaking havoc on his missions.

This latest film Christopher Nolan (“Memento,” “The Dark Knight,” “The Prestige”) practically defies description. It’s a metaphysical crime caper/action epic that unfolds almost exclusively in the dreams of its characters.

Dreams, of course, are where anything can happen, where the subconscious comes out to play or to torment itself, where our deepest fears are manifested.

In the near future of “Inception” our dreams can be invaded. Cobb (Leonardo DiCaprio) is a corporate spy skilled at “extraction.” Using a briefcase-size machine (it’s like a fancy lie detector with wires to connect the participants), he and his colleagues can enter the dreams of a sleeping target and root around for the deepest secrets.

This is no simple task. Cobb and his team create dream environments and scenarios so real that their drugged subjects don’t suspect they’re asleep, yet so subtly calibrated that they push just the right emotional and intellectual buttons. When subjects wake up, they have no memory of being violated; Cobb walks away with valuable information.

But Cobb is an international fugitive, accused of murder and unable to re-enter the U.S. to be with his two young children. This makes him vulnerable to the entreaties of the powerful industrialist Saito (Ken Watanabe), who recruits him to go after Fischer (Cillian Muphy), the heir to a rival conglomerate.

Instead of just extracting information, though, Saito envisions a far more dangerous “inception”: planting ideas into Fischer’s subconscious – ideas that would lead him to sell off his family’s extensive holdings.

If Cobb can accomplish this, Saito will pull strings to ensure his safe return home.

Nolan’s screenplay has two main sections. In the first, Cobb and his associate (Joseph Gordon-Levitt) recruit a new team – Ellen Page, Tom Hardy, Dileep Rao and Watanabe – and begin building the dream world in which they will operate.

The second half of the film is the actual job, and it’s truly mind-blowing, a labyrinth of dreams within dreams within dreams. The stakes are high. In a standard extraction, when a dream spy “dies” he simply wakes up in the real world. But should you die in the ever-deeper levels of an “inception,” you’ll find yourself in limbo, unable to return to our dimension.

Things are further complicated by Cobb’s own iffy mental state. Though he has kept it a secret from his colleagues, while on the job he’s often visited by his late wife and former extraction partner (Marion Cotillard), who may appear as a lover or as a gun-toting adversary. She’s obviously a manifestation of Cobb’s own tortured conscience, and her presence threatens everything.

Yeah, that’s a lot to wrap your head around. But Nolan is such a skilled storyteller that it all somehow makes sense. He finds ways to delineate between the ever-descending dream environments Cobb’s team must navigate so that we can sense just where we are at any moment.

And these dreamscapes make for some dazzling moments, like a brawl between Gordon-Levitt’s character and several thugs in a gravity-free hotel hallway. It’s like “The Matrix” on steroids… you can hardly believe what you’re seeing.

Shot across four continents by Nolan’s regular d.p., Wally Pfister, and outfitted by production designer Guy Hendrix Dyas, “Inception” is easily the director’s most visually unbridled work; its canvas stretches from the skyscrapers of Tokyo to the bazaars of Tangiers, from an amber-lit hotel corridor to a snowy mountain compound (a setpiece that plays like an homage to “On Her Majesty’s Secret Service”). Pic has arresting effects and images to spare, such as the sight of Paris folding in on itself like a book or Gordon-Levitt’s Arthur performing a fight scene in zero gravity (the explanation for which is even more dazzling).

“Inception” is a work of staggering imagination that’s almost undone by its very coolness. What it accomplishes is phenomenal. And yet on a fundamental dramatic level it feels vacant, an awesome display of filmmaking brio that offers plenty for the eyes, ears and head but precious little for the heart.

Nolan is a very clever fellow, no argument there. He’s skilled at juggling big ideas and making us think. Now if he can just make us feel.

A Warner Bros. release presented in association with Legendary Pictures of a Syncopy production. Produced by Emma Thomas, Christopher Nolan. Executive producers, Chris Brigham, Thomas Tull. Co-producer, Jordan Goldberg. Directed, written by Christopher Nolan.