Dave Lister is locked in stasis as punishment for smuggling a cat on board Red Dwarf.
While he's in stasis, a damaged drive plate releases radiation which kills the rest of the crew.
Three million years later, Dave is released from stasis by the ship's computer, Holly. He discovers that he's the last surviving member of the human race.
His only companions are a hologram of his least favourite crewmate, Arnold Rimmer, and the Cat, a life-form that has evolved from his cat.
The crew is joined in a later series by Kryten and by Kristine Kochanski (An old flame of Lister's).