You may have heard about Mindhunter, the new and highly anticipated Netflix crime drama. You may have heard that it's about cops trying to understand terrifying serial killers. In online promos and trailers you've seen you may have formed the impression, as you are meant to, that it's about appalling crimes.

What you may not have gathered about Mindhunter (which was set to begin streaming on Netflix on Friday) is that it is also very funny. Based on the first two episodes released to critics, the series is unnerving, incongruous and, at times, brilliantly made. Binge-watch this and you will be left reeling.

Set in the late 1970s, Mindhunter is about the beginnings of the study of serial killers, who weren't even called by that term at the time. One of the most jarring aspects of the series is the realization that, as recently as 1979, the science-of-crime material that underlies so much of TV and many movies, was unformed, unknown and scorned by the FBI. Back then, the idea of psychologically profiling serial killers and other criminals was something that made seasoned FBI agents snort with derision.

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Loosely based on the memoir Mindhunter by the man who changed all that, John Douglas, the series is written by British playwright and screenwriter Joe Penhall and the first episodes are directed by David Fincher, who made the movies Se7en and Zodiac and directed the first two episodes of House of Cards. Fincher's signature style of deeply muted colour palettes and almost subliminal signals of looming horror are on full display in the opening hours of Mindhunter.

After the credits, which are subtly disturbing, we are thrown into the world of Holden Ford (Jonathan Groff, from Glee), a junior FBI agent who teaches hostage-negotiation techniques to even more junior officers. He's tolerated in his insistence on the use of basic psychology but is told by a boss, "Psychology is for the backroom boys." Basically, he'll never get anywhere at the agency.

Undaunted, Ford takes university courses. The opening hour has a good deal of fun with the straitlaced young man mixing with university students and staff who see him as "a narc in a suit." He meets a young woman, Debbie (Hannah Gross, who is terrific), doing an MA in sociology and she teaches him a great deal about her field and women and sex. The answers to some of his questions begin to form. One of those questions is, "Where do we go when motive becomes elusive?"

This is a time period in which the Son of Sam killer has struck in New York and the world is still trying figure out what drove Charles Manson and his followers to kill. And Ford is immensely and charmingly curious about such matters.

Eventually, Ford thinks he's met a kindred spirit in fellow agent Bill Tench (Holt McCallany, in what is a breakout role after years as a solid character actor), a grizzled veteran who has been working as a one-man behavioural-science unit for the FBI but mainly teaching cops across the United States to be, well, a bit more thoughtful. "How do we get ahead of crazy if we don't know how crazy thinks?" Tench asks rhetorically. The pair are, in fact, the mismatched cops of cop-movie tradition. One is young and eager to learn, the other is world-weary and just wants to get the job done with a good buddy along for the ride.

The pair are travelling around California teaching cops when Ford has an inspiration: Let's talk to a particularly crazy killer and ask him about his life, motivations and crimes. It is here, in the second hour, that Mindhunter becomes truly unnerving. Tench scoffs and goes off to play golf but Ford goes to a prison and interviews Edmund Kemper (Cameron Britton). The Kemper figure is a real-life serial killer who murdered several young women and then killed his mother and engaged in necrophilia with her corpse. Kemper, an enormous man, is equal parts terrifying and charming. He's not Hannibal Lecter. He's a more mundane sort of monster, but uncannily skilled in understanding the mind of men like him. Ford becomes obsessed with learning from him. "It's not easy butchering people. It's hard work," Kemper says, and Ford is hooked.

That line about "butchering people" is used in the promos for Mindhunter, but it doesn't convey the incongruity of the relationship between Kemper and Ford. Ford is actually smitten with Kemper, a fact that discombobulates his girlfriend. Tench, however, is slowly convinced that Ford is on the brink of establishing an entirely new field in criminal psychology.

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It's hard to be firmly in favour of greatness in Mindhunter on the basis of two hours, but it sure looks like original and superior crime drama. It is unsettling to watch as Fincher toys with the viewer's expectations and has fun with the genre of mismatched cops working a crime. You'll find yourself amused by Ford's youthful enthusiasm clashing with Tench's wisecracking skepticism and, a minute later, horrified by the killer's languid recounting of gruesome murders.

Mindhunter is neither The Silence of the Lambs nor True Detective. It's not a procedural. It is, in a coolly dry way, a political drama – it's about a society's reluctance to understand why serial killers and mass killers are the way they are and why we are, at the same time, fascinated by them. It's about us, the audience, and it just might be one of the great TV dramas of the year.

Also airing this weekend

Sickboy (Sunday, CBC, 9 p.m. on CBC Docs POV) is a lively and eye-opening doc about Halifax-based yoga instructor Jeremie Saunders, 29, who has cystic fibrosis and has formed a unique perspective of life with a serious, debilitating disease. He looks ceaselessly for paths to eliminate the stigmas attached to all chronic illnesses. To that end, he started a podcast, called Sickboy, with his friends – in which he and others talk freely and often with humour about the challenges. "Laughing about disease takes away its power. I just want everyone to think that way, too," Saunders says.