This is the centenary year of Michelangelo Antonioni. He was born on 29 September 1912 and died in 2007 at the age of 94, having worked until almost the very end. As well as everything else, he gave us one of the founding myths of postwar cinema: The Booing of L'Avventura. For film historians, it's as pretty much important as the audience riots at the 1913 premiere of Stravinsky's Rite of Spring.

At the Cannes film festival on 15 May 1960, Antonioni presented his L'Avventura, a challenging and difficult film and a decisive break from his earlier work, replete with languorous spaces and silences. This was movie-modernism's difficult birth. The film was jeered so ferociously, so deafeningly, that poor Antonioni and his beautiful star Monica Vitti burst into tears where they sat. There was yet more booing when it got a special jury prize the following week. But nowadays Antonioni and L'Avventura get something more hurtful than boos: indifference. His great work, once a fixture of the Sight & Sound Top 10 list, this year plummeted out of the charts. This remarkable director has become a bit unfashionable: his kind of high European cinema doesn't command attention the way it did.

So who were those boo-ers anyway, those scarlet-faced, dinner-jacketed objectors? (The critic Alexander Walker once wryly told me they were standard-issue French bourgeoisie who didn't realise this wretched film was going to be so long, and were hungry for their dinner.) If they wanted to persuade the world that this emperor was naked, they didn't succeed. But were they just a bunch of grotesque philistines? Over past few months, I've been taking a look at this brilliant film-maker's body of work, and now I wonder if the booing isn't more complicated than I thought.

The title refers, ambiguously, to an adventure, or an affair. Antonioni himself was taking his audience on an adventure, away from conventional film-making, out into open waters, like the fateful boat journey in the movie's first act. Then he cut the motor, just as they were out of sight of land. However boorish, the boo-ers might just have been registering understandable dismay at the farewell to Antonioni's early "realist" period of the 1950s, in which he made conventionally paced and structured films, whose own mysterious brilliance has been forgotten. L'Avventura ushered in a phase of Antonioni's work for which he is well known and well parodied. But maybe the vast bulk of his career is effectively a kind of Jamesian "late" period, which shouldn't be allowed to overshadow those stunning first films. The 1950s classics: The Lady Without Camelias, The Friends, The Vanquished – these are the DVDs which I now feel like shoving into people's hands and saying: watch this.

The lady vanishes … Monica Vitti and Gabriele Ferzetti in L'Avventura. Photograph: Allstar/Cinetext/Criterion

In L'Avventura, famously, something mysterious happens and then, defying the rules of movie narrative, it refuses to un-happen. The mystery is unsolved. A group of well-to-do vacationers go on a trip to Lisca Bianca on Panarea, one of the Aeolian islands off the coast of Sicily; there one unhappy young woman, Anna (Lea Massari), vanishes and her perplexing disappearance brings together her fiance Sandro (Gabriele Ferzetti) and best friend Claudia (Vitti) in a doomy and melancholy affair in which they experience a kind of existential fear – and appreciate the advantages of non-being. As for Anna, she might theoretically have just run away, escaped from a marriage she was dreading and become another missing-person statistic. But it could also be that this island, like the mysterious Australian rock formation in Peter Weir's Picnic at Hanging Rock or the Marabar Caves in EM Forster's A Passage to India, have somehow become the epicentre of occult metaphysical crisis. Anna has dematerialised. Her atoms have been blown away in the wind. She has had a very human yearning for absence, for the annulment of all the cares that torment her. All this, in a kind of anti-miracle, has been granted her.

There are some extraordinary set-pieces. The final sequence in the hotel foreshadows the nightmare-puzzle of Alain Resnais's Last Year in Marienbad (1961) and the bizarre scene in which vast, excitable crowds in Palermo mob a sexy celebrity writer called Gloria Perkins is very like that in Godard's Breathless (1960), in which Jean Seberg's Patricia goes to interview the famed author Parvulesco, played in cameo by Jean-Pierre Melville. L'Avventura surely influenced Michael Haneke and the Iranian director Asghar Farhadi.

I am a bit more agnostic about the movies that followed. La Notte, or The Night, in 1961 has wonderful performances from Marcello Mastroianni and Jeanne Moreau as Giovanni and Lidia, the unhappily married couple in fashionable society who attend a smart all-night party, their mood drenched in ennui and clouded by Giovanni's obvious infatuation with another woman – again, Monica Vitti. But I found the ending contrived and contorted. The Red Desert in 1964 was Antonioni's first colour film and I think one of the best of his "high" period of opaque existential anxiety. Vitti is the industrialist's wife who is suffering from depression following a car wreck, and the brutal, polluted landscape makes northern Italy look like another planet, like the Paris of Godard's Alphaville (1965).

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Antonioni's three English-language films come after this, and here is where I part company from many pundits. Blow-Up (1966) is the swinging-London tale of a fashion photographer, played by David Hemmings, who accidentally takes a photo of a murder in a London park, and only realises it when he begins to enlarge the background in grainy detail. It's is a metaphysical mystery in what critic Richard Hofstadter called the "paranoid style", perhaps inspired by the endlessly scrutinised Zapruder home-footage of the Kennedy assassination. Now I have to admit something: I've often felt like booing the weak ending – which offers neither conventional plot resolution nor an interesting restatement of metaphysical mystery. Hemmings's scrutiny of the photographs is revealed with a superbly disturbing sequence of black-and-white still images, accompanied by the eerie sounds of the wind in the trees remembered from the park. But the rest of the movie is distended with a series of wacky vignettes and redundant action, including a superfluous if entertaining and atmospheric scene in which Hemmings finds himself at a secret concert given by the Yardbirds in a basement club off Oxford Street.

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The second and third English-language movies are far superior. Zabriskie Point (1970) is Antonioni's fascinating film about hippy protest and radical counterculture in late 60s America, a bad trip – very freaky, in a drawn-out, Antonioni-esque way – with its own premonition of the violence at Kent State. It urgently captures the times, with some great documentary-realist crowd scenes, very American, and yet the fugitive love affair at its centre is very Godardian. I have never seen a film which fuses European and American sensibilities so well, and the final apocalyptic vision of an explosion of consumer goods is a brilliant dream-spectacle.

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Zabriskie Point got Antonioni awful reviews in the US, but in many ways it's one of his most daring and experimental movies, though overshadowed by the star-power of The Passenger (1975), with Jack Nicholson as Locke, the world-weary reporter who vanishes – as in L'Avventura – by filching the identity of a dead stranger who turns out to be an arms dealer, and whose own inevitable death Locke must now calmly, even ecstatically accept.

As for the rest of Antonioni's films, my neurotically completist mission to see all the features yielded a mixed set of reactions. His Chung Kuo – China (1972) is a punishingly long, three-and-a-half-hour documentary about that country which often looks like nothing more than a rather naive travelogue-cum-home-movie. But there is real archival interest there. The 1981 feature The Mystery of Oberwald, based on Cocteau's play The Two-Headed Eagle, was pioneeringly made on analogue video, with weird filter effects, though it now has the flat look of a laborious television play. (In fairness, I should say I could only locate a fuzzy VHS copy.) It certainly doesn't deserve to be forgotten, though, as it features Vitti's most mature and developed performance, as the queen who falls in love with a would-be assassin who was a doppelganger of her late husband.

After this, Antonioni's career is something of a long goodbye. He began to take an interest in eroticism. His Identification of a Woman (1982) features some notably explicit sex scenes and, disconcertingly, it does look a little like a porn film. Antonioni suffered a stroke in the mid-80s, but it was a testament to his energy and stamina that he was able to keep writing short stories, and returned with his final film Beyond the Clouds (1995) based on some of his stories, made with the assistance of Wim Wenders. Again, it has a rather softcore-erotic feel. But it interestingly restates the themes of Blow-Up, as its lead character, played by John Malkovich, says: "I only discovered reality when I began photographing it, photographing and enlarging the surface of things around me …" Marcello Mastroianni and Jeanne Moreau are brought back for a moving cameo as an elderly couple.

And so Antonioni gradually faded from view, a shadow of his former self, whose last work in 2004 was a pallid short film contributed to a collection called Eros – a film whose supposed eroticism was unconvincing.

So now it is a really thrilling experience to return to the almost-forgotten prehistory of Antonioni, those punchy, cerebral but often highly experimental realist pictures of the 1950s, beginning with the Greeneian, downbeat Story of a Love Affair (1950), about a forbidden relationship rekindled by the snoopings of a private detective. The film precedes by one year the publication of Greene's The End of the Affair and in its seediness resembles Patrick Hamilton's Gorse novels, or Gerald Kersh's Night and the City.

The Lady Without Camelias

Antonioni's The Lady Without Camelias (1953) is a wonderful film, and in fact my favourite of his. It's a brilliant tragicomedy about the movie business: the missing link between Truffaut's Day for Night (1973) and Sturges's Sullivan's Travels (1941). I think its desperate sadness and emotional maturity entitle it to neglected-masterpiece status. Lucia Bosé plays Clara, a former shop assistant from Milan who has been discovered by ambitious movie producer Gianni Franchi (Andrea Checchi). Without ever consciously choosing a film career, or being in any way happy or fulfilled in it, she is swept up into huge commercial success in light musicals and comedies. Poor Clara and her husband become obsessed with getting her into classy, quality cinema – a delicious irony, given Antonioni's own spectacular career arc. Clara's tragic destiny is to confuse love and contentment with a successful career in arthouse cinema: she has a fatal delusion that success in high art – just out of reach – is crucial to human happiness and self-respect. What a glorious film it is, Chekhovian in its wit and melancholy.

The Vanquished (1953) is a captivatingly strange portmanteau film, featuring three brash and anxious tales from France, Italy and England, ripped from the newspaper headlines. Moody and alienated young delinquents are killing for thrills, for celebrity, for the sheer Dostoevskian hell of it. The Italian segment gives the clearest indication so far of the way Antonioni's film-making was going to develop. After killing a customs officer, a young man runs desperately away and falls, hitting his head. From here, he wanders around in a daze, not entirely lucid. His meanderings are a hint of the strange phases and altered states of L'Avventura.

In The Friends (1955) a young woman called Clelia arrives in Turin to manage a new fashion house; she is played by Eleonora Rossi, with a resemblance to Ingrid Bergman. On her first night, she is shocked to discover the woman in the hotel-room next to hers has attempted suicide: this is Rosetta (Madeleine Fischer). At once, Clelia finds herself involved in the life of Rosetta's circle of excitable, mercurial friends. It is as almost as if these friends sense that, however much Rosetta recovers from her suicide attempt, she is now absent, and that Clelia is being groomed as a replacement "friend". It is a brilliant and disturbing serio-comedy, gossipy, soapy, melodramatic.

The Cry (1957) shows Antonioni beginning to morph into the famous creator of the later movies. Aldo (Steve Cochran) has a furious row with the woman with whom he has had a child. He leaves and takes their daughter with him, on a quest to find a woman who could possibly be a replacement for his lost love and a mother to his girl. He wonders if he can make a new life for himself, perhaps efface his catastrophic life choices. Aldo is electrified by the tall tales of a dredger captain he meets, who says he made a modest pile working in Venezuela. Aldo actually goes so far as to get a map of that country, with some sort of booklet showing employment opportunities for a skilled mechanic. But then, on a despairing whim, a sudden, bleak realisation that this is all nonsense, he simply throws the map and the papers away – they flutter off on the wind. It is a superb, rather literary moment. Here is where the existential fume of Antonioni's work begins to be distilled: from the bones of plot arises the smoke of anxiety, disenchantment, alienation – but also a numbed kind of rapture and release at human helplessness.

So this is my essential Antonioni viewing list, divided into early and late, or perhaps pre-Boo and post-Boo. All of them are the work of a master, and yet if I had to recommend one to start off with, it would be The Lady Without Camelias. You can't appreciate what a strange and wonderful director Antonioni is without watching that early gem. I think it is through a rediscovery of these early classics that Antonioni's reputation will rise once more.

Early Antonioni

La Signora Senza Camelie (The Lady Without Camelias) (1950)

I Vinti (The Vanquished) (1953)

Le Amiche (The Friends) (1955)

Il Grido (The Cry) (1957)

Late Antonioni

L'Avventura (1960)

Il Deserto Rosso (The Red Desert) (1964)

Zabriskie Point (1970)

The Passenger (1975)