“It Follows,” a new horror film, self-consciously follows the horror cinema that went before it. That goes for movies as well as stories that probably date to ancient times. It’s a primal tale. The creepy atmosphere writer-director David Robert Mitchell gives the film is among the better “It Follows” qualities.

The story begins with a jolt. A terrified young woman flees from her home as if someone, or some thing, is pursuing her. Her concerned father asks what’s wrong. “I’m fine, dad,” she says, not telling the truth.

The movie’s principal character, another young woman, makes her entrance while swimming in the family’s backyard pool. That night, Jay (Maika Monroe), a 19-year-old college student living in a bland Detroit suburb, has a date. She’ll have a second date with the same guy soon thereafter.

An abrasive synthetic keyboard provides the “It Follows” soundtrack. More silly than eerie, the synthesizer music is a homage to “Halloween,” a classic horror film about an earlier generation of teens pursued by relentless evil. In “It Follows,” Jay and other teens are similarly hunted.

Jay’s nightmare begins after her second date with Jeff (Jake Weary). The date includes sex and terror. The principal plot device in “It Follows” is a curse, though not explicitly named as such, that’s passed through sexual intercourse.

“It’s going to follow you,” Jeff warns Jay. “Somebody gave it to me and I passed it on to you.”

Like many late 20th-century horror films featuring teens, the young people who engage in sexual relations in “It Follows” unwittingly put themselves on a short list for slaughter.

Jay, and anyone she infects with the curse, has the disadvantage of not knowing what human form the murderous stalker will appear. “It” can look like anyone, Jeff explains, including the people most close to her.

There’s slight relief in that It moves slowly. For all of It’s single-minded similarity to Michael Myers, Jason Voorhees and Freddy Krueger, this silent stalker also suggests the classic, foot-dragging Universal Studios monster played by Boris Karloff in 1932’s “The Mummy.” Even with one arm strapped to his chest, the Mummy always gets his man — or woman.

“It Follows” follows another unwritten rule of monster movies. Jay’s friends, who can’t see It, don’t believe the monster exists. “What exactly is supposed to be following you?” Jay’s friend, Paul (Keir Gilchrist), asks.

Writer-director Mitchell doesn’t linger on the skepticism. Jay will not fight the fight of her life alone. “It Follows” becomes an ensemble movie as Jay’s sister, Kelly (Lili Sepe), and loyal friends, the nerdy Yara (Olivia Luccardi) and Paul, gather around her.

Jay’s friends apparently have a penchant for watching cheesy black-and-white sci-fi movies on TV. Mitchell is a wry filmmaker with a minimalist, low-fi touch and, no doubt, he had a small budget for “It Follows.” At times, his latest film looks hokey and cheap. Other times the imagery is brilliant and chilling. The best stuff in “It Follows” feels like a tempting prelude to what the film’s young director will do next.