In the first episode of Netflix's Mindhunter, a young FBI agent in training observes that cadets spend more time on the gun range than they do studying behavioural psychology. Because why try to understand a killer when you can just shoot them? It's the dark question at the heart of David Fincher's second production for the streaming service, following House of Cards. While the veteran director has recently moved further into the TV realm, Mindhunter is more reminiscent of his film work, especially Zodiac and Se7en. The guy excels at exploring the dark side of humanity; how virtuous characters are affected by their encounters with wicked people.

And those wicked people are frequently serial killers. Or "sequence killers" to be more precise, because Mindhunter is set in 1979 and the former term hasn't been invented yet. The ten-part series is based on the true story in the book Mind Hunter: Inside the FBI's Elite Serial Killer Crime Unit by Mark Olshaker and John E. Douglas. Douglas pioneered the method of building psychological profiles of killers, so detectives could anticipate their next move or narrow down a list of suspects. The book was adapted by screenwriter Joe Penhall (The Road) and playwright Jennifer Haley (The Nether), who consolidate several key figures in the true story into three main characters: two FBI agents (Jonathan Groff and Holt McCallany) and a psychologist (Anna Torv).

In 1979, of course, America is still quaking in the aftermath of Watergate and the Kennedy assassination. David "Son of Sam" Berkowitz is behind bars after murdering six people in New York City and claims his dog told him to do it. Charles Manson is a fresh inmate and the summer of love has disintegrated. The FBI is baffled by a growing list of men who kill without any clear motive—a terrifying, and new, prospect. As an expert on Berkowitz points out: "We are staring into a void." The world is changing and the top law enforcement agency is struggling. America is losing its mind.

So Mindhunter, uh, goes about finding it. The show focuses on an understaffed FBI behavioural science unit that interviews serial killers and applies the knowledge gained to ongoing cases. We know now that empathy can save lives, but the 1970s FBI thinks it's a waste of time.

Mindhunter is about obsessive people on each side of the law and so makes perfect source material for Fincher, who has been consumed by psychological thrillers throughout his career. Se7en shows the hopeless moral erosion of two police officers in the pursuit of a serial killer. Fight Club looked at emasculation in the midst of a capitalist 90s culture and used The Pixies to ask the "Where is my mind?" question, and Gone Girl gave fangs to the sordid lives of privileged white Americans and their mangled interpretations of marriage. Then there's Fincher's greatest passion project, Zodiac, about the decade-long manhunt for one of America's most notorious serial killers, which remains an unsolved mystery.

Like any police procedural, Mindhunter focuses on the odd-couple pairing of two agents. McCallany is great as a tough guy caught between a new wave of intelligent casework and the working class ideals of the traditional police force. Groff is a little stilted as an FBI trainer going from the classroom to Q&As with killers. In the initial episodes the scenes that work best place McCallany and Groff together on the road, debating the merits of their work. It's the perfect combination of realism and idealism.

The most chilling scenes feature encounters with the killers. At first the FBI views these men as unreasonable savages, but they inevitably turn out to be articulate, intelligent and extremely manipulative. One of the first encounters is with Edmund Kemper (Cameron Britton), a killer known for decapitating his victims and then engaging in necrophilia. He was a real guy—Google him and let the nightmares begin. Edmund seems like a friendly gentle giant, but as time goes by the agents realise they are caught in a game of wits with someone far more cunning than he appears.

The show is set in a white, male-dominated world, mainly because of historical context but also because the series has something interesting to say about what drives privileged men to become deranged. It's a foggy search for answers that often concludes with horrific stories of childhood trauma, abuse, or sexual shame. There's an overbearing sense of the old school masculinity and sexual repression that's destroying the minds of these men at the end of a turbulent decade of change.

My partner told me to turn up the brightness while watching Mindhunter, because Fincher stays true to his nickname: the prince of darkness. As with every Fincher production, the direction is immaculate and precise. The camera moves like it was calculated to land in the exact spot, down to the micro millimetre. The design of the series is minimalist without going over the top to remind you it's set in the 70s and the cinematography, by Erik Messerschmidt and Christopher Probst, evokes the sepia-toned work of Harris Savides in Zodiac. Fincher's trademark shadows stalk every frame.

If you have a Netflix subscription you are being spoiled with Mindhunter. Don't perceive this series as Fincher taking a step back from film to ride the popularity of streaming services. Mindhunter is like a companion to Zodiac, and based on first impressions it's essential viewing for Fincher fans and anyone fascinated by true crime.

Still, it's hard to see how the show—which has already had its second season greenlit by Netflix—will offer closure. History tells us the FBI eventually finessed their techniques to profile and track serial killers, but an ability to comprehend acts of evil still evades us. Looking at recent news headlines around mass shootings in America and acts of terror in Europe, the themes of Mindhunter become contemporary. The Talking Heads' "Psycho Killer" plays at the end of episode two—a little on the nose. "Psycho killer, qu'est-ce que c'est" famously translates to "Psycho killer, what is that?" We still don't know.

'Mindhunter' streams on Netflix from October 13