The Royal National Theatre of Great Britain played a one-night stand in the Valley last month. It went so well they’re making a return visit this Sunday.

The performance of Shakespeare’s Hamlet was, of course, the latest in the NT Live series—satellite broadcasts of live performances from the National’s stage to movie screens around the world, including the Amherst Cinema and Pothole Pictures in Shelburne Falls. The technology includes not only high-definition big-screen images, but multi-camera videography that puts cinemagoers right on stage with the performers. The screenings have proved so popular that Amherst Cinema schedules an encore showing of each play.

Nicholas Hytner’s production of Shakespeare’s most intimidating play is intelligent, accessible and unapologetically modern. Prince Hamlet sulks around in jeans and a hoodie, military jets are heard roaring overhead, and there’s not a bare bodkin in sight before the climactic fencing match. The closed society of Elsinore Castle is reimagined as the seat of a contemporary police state controlled by constant surveillance and implicit violence. Anonymous gray-suited men with wires in their ears stand sentinel on the fringes of every scene, and every private conversation begins with a glance over the shoulder. Only in soliloquy can the prince’s tormented thoughts find a safe outlet.

The concept is surprisingly apt, chillingly evocative of our own monitored society but faithful to Shakespeare’s claustrophobic vision. In a scene that’s usually cut, old Polonius sends an agent to shadow his son Laertes at college. And what else are Rosencrantz and Guildenstern, summoned by the king to pry into Hamlet’s seeming madness, but spies?

Lines often overlooked take on fresh meaning here. “You are a fishmonger,” taunts Hamlet, and when Polonius objects, he adds, “Would you were so honest a man.” Themes of truth, deception and hypocrisy take center stage in this robust production and add grit to the person-to-person drama.

Patrick Malahide as King Claudius is a steely, business-like tyrant; Clare Higgins an unusually strong-minded Queen Gertrude; Ruth Negga a feisty Ophelia whose death is not grief-induced suicide but an administrative murder because she’s an embarrassment to the state. Rory Kinnear’s Hamlet is an ordinary-looking prince with an adolescently messy bedroom and an intellect, expressed in cruel humor and spontaneous compassion, that strives frantically against circumstances that “puzzle the will.” It’s a mercurial, complex performance that both underscores and contests the production’s air of paranoid menace.

The prince’s “antic disposition” also finds moments of pointed humor. Having described Claudius, his father’s killer, as a man who can “smile, and smile, and be a villain,” Hamlet scrawls a smiley-face on the wall with the inscription “Villain,” and then turns up wearing that subversive logo on a T-shirt.

This year’s NT Live productions include two by other British companies. The season opener, A Disappearing Number, was performed by the experimental Complicite company, and next month’s King Lear, starring Sir Derek Jacobi, comes from London’s intimate Donmar Warehouse. Next up is a musical, Fela!, about Afro-pop musician and activist Fela Kuti, and the season rounds out with new adaptations of Frankenstein and The Cherry Orchard.”

Hamlet: Jan. 9, 1 p.m., Amherst Cinema, Amity St., Amherst, 253-2547, amherstcinema.org.

Fela! Jan. 13, King Lear, Feb. 3, 7 p.m., Amherst Cinema and Memorial Hall, 51 Bridge St., Shelburne Falls, 625-3052, www.shelburnefallsmemorialhall.org. Repeat showings at Amherst Cinema Jan. 30 and Feb. 27.