norwegian First unveiled in 1893, Edvard Munch's The Scream is one of modern art's landmarks. Its skull-shaped, foetus-like visage with the anguished gaze made its Norwegian creator infamous until he died. To this day, however, pundits still debate what it shows. Is "The Scream" an existential howl? A tortured self-depiction? Or just the marketing of misery by a talented victim?

Illustrator-cartoonist Steffen Kverneland has also wondered. A fellow Norwegian born in 1963, Kverneland bought his first serious book on Munch at age fifteen. This was a year before he started to create comics, initially publishing strips in the humour magazine KOnk. In 1993, his first album De knyttede never ("The Clenched Fists") was named Norway's comic of the year. By 2011, critics knew him as part of the country's comics renaissance.

Kverneland's style is a brassy and bold one – distinguished by taut lines and boisterous, gonzo graphics. But the artist, who is also a wonderful portraitist, has engaged in several projects that make great lives accessible. Previously he has worked on the likes of Poe and Ibsen. Yet, over the years, he slowly inched closer to Munch.

Kverneland decided to tackle Norway's titan in 2005. Although there have been countless Munch biographies, he felt the comic-book format held new possibilities. To up the ante, Kverneland made a central, radical choice: in place of reported speech, Munch would tell his story. The artist would be heard only in his actual voice.

It was a Dogma 95-style decision, a search for reality using only primary sources. Kverneland knew Munch had been an epic scribbler and that he was close to writers such as Ibsen and Strindberg. During the 1880s, too, Munch had worked with graphics and text – keeping a journal Kverneland describes as "a proto-BD". Yet the author's decision meant Munch took seven years to complete.

Now available in five languages other than French (and, hopefully, in English soon!), the book has become an award-winning hit. Munch caused a special sensation when – as a work of non-fiction – it won Norway's Brage Prize for Literature. Much of its artwork sits in the country's National Gallery of Art.

Such acclaim is no surprise. Munch is a dazzling use of sequential storytelling, one that look leaps back and forth in time while madly swapping styles. It features a Rolodex of visual registers which includes quirky takes on Impressionism, Cubism, Expressionism, Art Nouveau and fin-de-siècle salon painting. There are allusions to filmed cartoons and silent cinema, as well as plenty of collage and modern photography. Most of these different approaches help to indicate time or character.

Technically, our source for the story is Munch as elder statesman. But the book also features Keverneland himself – in tandem with a fellow wild-man cartoonist, Lars Fiske. Like modern embodiments of Munch's Bohemian buddies, this pair step in to joke and argue about what really happened. As the pages speed by, they smoke, dine, drink like fish and disagree about Munch's life.

Fiske and Kverneland have worked together for more than a decade. In 2004, for No Comprendo Press, they employed similar tactics in creating Olaf G. Slated to be published in English by Fantagraphics, this is the story of master caricaturist Olaf Gulbransson. In Europe, it launched the authors as a comics double act. Like an out-of-control Dupuy and Berberian, their on-the-page personas rarely appear sober. Whenever the self-caricatured duo finally settles down, the discussion revolves around one thing: art.

Within a year of Olaf G, each started a new biography. Kverneland's target was Munch and Fiske's was the Dada great Kurt Schwitters. (Fiske's story became Herr Merz, published in 2013 by No Comprendo). In order to fund and showcase such long-term projects, the artists launched Kanon: an album of their own. Since 2005, it has published five editions, each of which allowed peeks at Munch and Merz in progress.

Anyone who flips through a copy of Munch can see that it's singular; you don't even have to be able to read it. Although the painter's early life was one of legendary miseries, the album bursts with visual humour and ocular pleasure. Its artist subject never sought to copy reality ("I don't paint what I see; I paint what I saw", Munch would say) and the volume does that legacy justice. Munch tried hard to capture how memory marks the psyche, and his art always tried to access deep emotions. Using his own medium, Steffen Kverneland does the same.

Certainly, the project gives him plenty of drama to work with. Circumscribed by illness, death and strict religion, Edvard Munch's early years were both sad and sequestered. At five, he lost his mother; a decade later, his favourite sister – each of them dying slowly in front of him. Between these two events, at the age of thirteen, even Munch himself was given up for dead.

Yet, once he survived and set out to paint, the prodigy had support from what remained of his family. Two of Munch's relatives were well-respected painters and the post-Impressionist Paul Gauguin was a distant in-law. Thus when he first visited Paris, Munch was more than just another rube. In 1889, at the Universal Exposition, he got a first-hand look at French art's past and present. But what proved most important were the things Munch saw around town: new sculptures by Rodin, paintings by Van Gogh and the strong lines in posters by Toulouse-Lautrec.

Kverneland covers many of Munch's formative circumstances. But the book's focus – its "present" – is avant-garde Berlin during the 1890s. Here, Munch held what would remain his best-known exhibition, equal parts artistic breakthrough and enormous scandal.

While Kverneland draws the painter's past on a rough brown stock, all those Berlin days are rendered in colour. As our elderly narrator, Munch is realistically drawn; he's a tired, black-and-white photo brought to life. Other moments and characters have stylistic codes of their own – but all inhabit a visual world infused with 'Munch-like' character.

Kverneland says that reproducing Munch's own art was a special pleasure, one he describes as semi-addictive and "almost autistic". Yet his turns on the artist's style offer both flair and inventiveness. Leavened by the impudence of Kverneland and Fiske, Munch is very often laugh-out-loud funny. But when it comes to family (or the real-life toll of debauchery), its pages can shift abruptly toward the poignant.

What helps Kverneland enormously is his cast of characters. Non-Scandinavians won't know the bohos who formed a youthful Munch so, in a tableau, their figures are decoded. (To show who is in love with whom, it features hearts and arrows.) As artistic rebels, though, the artist's first pals are very familiar: it's a stereotypically narcissistic, hard-living crowd.

Their leader in Christiania – later Oslo – is writer Hans Jaeger. Jaeger was an anarchist who was to remain Munch's great mentor. He once boasted he would corrupt his entire generation or, failing that, he would "drive them all to suicide".

There was a lot with which these rebels might have disagreed. Although Norwegian society was officially Lutheran and bourgeois, one-third of its labour force consisted of underage children. Its Christian family men were served by state-run brothels – where prostitutes, to protect the clients, got regular, rigorous checks. Yet Munch's Bohemian crowd remained self-centred and their transgressive efforts focused only on personal trauma. Just like drink and sexuality, suffering was their subject and – as Munch was quick to learn – the more personal pain, the better.

Kverneland has a lot of fun with the truth behind Munch's image. Instead of the misogynistic, sad-sack Bergman of the canvas, readers will discover the artist as an ambitious go-getter. Unflagging when it comes to his self-promotion, the Norwegian proves both canny and resourceful. Says Kverneland, "Once I started reading everything Munch wrote, I found him enormously funny, ironic…and optimistic".

Here Munch always leads with his impressive chin and, despite a frequent lack of funds, is feisty and competitive. Only when it comes to sex is the painter ever timid. There he is haunted by his early exposure to suffering – as well as by a father who remains demanding and dogmatic. Munch retaliates through a willful life of debauchery. Yet, unlike his friends, the painter keeps a watchful distance.

As Kverneland shows, childhood left Munch with unsettled spiritual questions and, in his heart, the era's solipsism puzzled him. Yet his main solution was to keep on drinking – while, over and over, he used art to re-play traumas.

Halfway through the album, we discover a link between Munch's story and that of his author. Next to a frame in which he appears dressed as the painter, Keverneland introduces the section on Munch's childhood. It was, he tells Fiske, difficult to draw. "All around him, his family was falling like flies and, in my family, it was the same. Now there's no one left but me. So I sympathise with him… at times, it's been a substitute for writing my autobiography." Every time he draws the young Munch, adds Kverneland, he reimagines his lost brother Tore.

The book's motley cast is deliciously exotic and it contains some truly ferocious eccentrics. One is the beautiful, ruthless Dagny Juel – partly responsible for the femmes fatales Munch loved to paint. Briefly the artist's lover (she abruptly dumped him for Strindberg), Juel flits from man to man until she is gruesomely murdered. Equally licentious is her husband "Stachu" Przybyszewski. A Polish piano whizz who wrote the first book on Munch, Stachu is a womaniser, a pathological drunk and a Satanist.

After Munch, however, the most dynamic figure is Strindberg. The temperamental Swede is usually known for his plays (Miss Julie, The Dance of Death, Ghost Sonata, etc). Yet he was also a poet who tried his hand at painting – and he was the artist to whom Munch felt closest. Both creators believed in ghosts, both led haunted lives and each was determined that his work would incorporate chance. As Munch shows with brio, both were advance Surrealists.

Strindberg is drawn with the author's finest comico-Cubism. But, from moment to moment, it changes dramatically – just like his chaotic psychology. During a nightmare, for instance, Strindberg starts to strangle his wife. So the representation switches from colour gouache to black-and-white woodcut. Later, when Strindberg's mind finally does collapse, his facial tectonics bulge to the bursting point. Yet our final view, seen through the eyes of Munch, is created with the most compassionate naturalism.

While Kevrneland leads us through streets, studios, dreams and brothels, Munch is transforming his rakish days and nights into art. The results are all icons we can recognise: Madonna, The Vampire, The Sick Child and, of course, The Scream. The reader learns how all Munch's various friends contributed, but it's very clear what perceptions came from him.

For those who love art, comics or just great storytelling, there's much more to relish inside Munch. Not only is its visual presentation a tour-de-force. The big surprise is how Kverneland subtly shows us something ineffable. His book captures art's essential, accretive genesis – how, over time, many separate moments and events can cohere into something original. The Scream's long evolution takes up more than fifty pages. Yet, at the same time, it's the book's true story.

Rarely have I read a more entertaining biography. It's a work I picked up knowing a fair amount about Munch, yet with no real interest in him. Now, just like Kverneland, I'm really going to miss that chin.