Research into the "serial killer mind" generally identifies four primary typologies: Driven by voices or visions (often psychotic).
There is no single "profile." They come from all backgrounds and often lead perfectly normal double lives as parents, coworkers, or neighbors. Inside the Minds of Serial Killers: Why They Kill Inside the Minds of Serial Killers
Depending on what you're looking for, these books are the most prominent resources under this title: Research into the "serial killer mind" generally identifies
Belief that they are "cleaning up" society by targeting specific groups. Inside the Minds of Serial Killers
A highly-regarded academic yet accessible study that dispels myths (e.g., that all serial killers are "geniuses") and categorizes motives like lust, thrill, profit, and rage.