In the town of Mapleton, N.Y., all appears normal. The shops on the Main Street are open for business, and the neighborhoods are full of pristine homes and well-manicured front yards.

Except something has gone terribly wrong in this fictional town in the HBO series “The Leftovers.” Three years earlier, 2 percent of Mapleton’s — and the world’s — population mysteriously vanished. Nothing has been truly normal since.

A ghostly cult silently stalks the town, chain smoking. Feral dogs roam the streets. And as conspiracy theories ricochet through the country — if the mass disappearance wasn’t the Rapture, just what was it? — shadowy organizations emerge, their intentions unclear. In the midst of all this, the police chief — whose own family has been fractured by the departure — tries to hold both the town and himself together.

“The Leftovers,” which debuts on HBO on June 29, is not a David Lynchian exploration of small-town evil. The creation of Damon Lindelof and Tom Perrotta, based on the novel of the same name by Mr. Perrotta, it is an intimate family drama that traffics in issues like faith and loss and grief and how to proceed after an enormous tragedy.