Pictures cut from five decades of Life magazine …Geoffrey Farmer’s Leaves of Grass at Documenta 13. Photograph: Ralph Orlowski/Reuters

A gentle but relentless breeze, courtesy of British artist Ryan Gander, blows through the Fridericianum in Kassel, one of the world's oldest museums. Three small sculptures by Julio Gonzáles, first shown at the second Documenta show in 1959, stand in the draught. It's the wind of history, an air of uncertainty and impermanence. We are blown about.

Kassel's history and Germany's are unavoidable at Documenta 13, which opened on Saturday. The show fills the city, from the train station to Karlsaue park, from Kassel's museums to its theatres and cinemas, from houses to hotel ballrooms. Documenta takes place every five years, lasts 100 days, and features 200 artists. You might even be tempted to travel further: to Kabul, where an Afghan outpost of the exhibition continues; or to Alexandria, Cairo and Banff, where more related events are taking place.

Tacita Dean has brought the mountains of Afghanistan to Kassel, filling a former banking hall with enormous, beautiful blackboard drawings. Some are near-empty, just turbid blackness; others are filled with moiling rapids and rushing rivers. There are sunlit mountaintops, dusty avalanches, chalky wipe-outs. The six panels are a sort of storyboard, an evocation of an elsewhere. Dean's drawings are, I think, about time: geological time, the flash of a life, a passing thought.

"I'll just keep on till I get it right," sings Tammy Wynette, in a snatch of song by Ceal Floyer. Over and over Wynette sings the phrase. In a nearby room hang still lifes by Giorgio Morandi, among some of the vessels and objects he painted and repainted, year after year, in his dusty room in Bologna. Morandi was always doing the same thing, but always making it new. Documenta is full of such interruptions: new and ancient things, the living and the dead, mysteries and miseries.

Here are 400 beautiful, modest postcard-sized paintings of different varieties of apple, by Bavarian pastor and artist Korbinian Aigner. Imprisoned for his anti-Nazi sermons, Aigner worked as a gardener in Dachau and Sachsenhausen, where he cultivated several new varieties, one for each year of his internment. There's pathos here, among these rows of painted apples.

I sense a theme: repetition, perhaps, the endless return. But as soon as you grasp for it, it is snatched away in favour of something else. Here are some chips of rock, fragments of the Bamiyan Buddhas, destroyed by the Taliban in 2001. And there a bag of marble dust – actually carved from a single chunk of marble by Sam Durant. And after the apples comes a room of hi-tech devices, working experiments devised by quantum physicist Anton Zeilinger and the physics faculty at the University of Vienna. The machines wink, dials twitch, numbers gabble across screens. One needs to make time to pause, even though these are things I shall never understand.

Beautiful, modest postcard-sized paintings … Korbinian Aigner’s apples. Photograph: Jens Meyer/AP

So much can be found in a single image or object. There's a whole history in Lee Miller's photograph of herself taking a bath in Hitler's tub at his Berlin apartment. At the Neue Galerie, a whole century seethes in Geoffrey Farmer's Leaves of Grass, a vast field of grass whose leaves are thousands of pictures cut from five decades of Life magazine.

Documenta was founded as an adjunct to the local horticultural show in 1955, devoting its first exhibition to Entartete Kunst, the art the Nazis had deemed degenerate. Since this modest beginning, Documenta has grown in importance. It is above all serious, and tries to stay away from the flim-flam of artworld tourism and junketing. There are unforgettable moments in the current Documenta, confrontations that thrill me, speculations that unnerve me, places (as well as artworks) that haunt me.

Documenta also has its funny side. Somehow, I got myself coerced into a bizarre and incomprehensible live game show played inside a mountain of mud, devised by Michael Portnoy. Out of 30 contestants, I won. The only prize was the opportunity to leave. The questions were pure psychobabble, as were the answers. Somehow my use of the word floccinaucinihilipilification clinched it, while also neatly describing the ludicrous event itself.

One of the most astonishing moments comes as you wander the vast landscaped park between the city's museums and the river. Among the trees are mounds of broken-up asphalt and Tarmac. There are craters, puddles, muddy paths. It is as if some great work was begun here, then interrupted. Great stands of nettles and strange plants flourish: nightshade, poisonous legumes, convolvulus, digitalis, Afghan poppies, cannabis, aphrodisiacs, psychotropic plants.

In a clearing at the centre of this enclosed world sits a statue of a reclining woman, whose head writhes with bees, like thoughts buzzing. Somewhere, too, is a man, drawing his surroundings; and two lithe Spanish greyhounds, one of whom has a leg dyed pink. It's all wonderful and mysterious. I confess I never actually saw the dogs, though I came here twice. It was disappointing, but gave the creatures a mythical status as I searched among the craters and spoiled earth, the overgrown earthworks and an uprooted Joseph Beuys oak tree. Somehow, I felt a terrible sadness at being in the world. It was like being in an abandoned battlefield. This is all a work by France's Pierre Huyghe. "Live things and inanimate things, made and not made," reads Huyghe's description of his materials.

Thoughts buzzing … Pierre Huyghe’s bee-headed woman. Photograph: Barbara Sax/AFP/Getty Images

I stand at the end of a station platform at the Hauptbahnhof and listen to Susan Philipsz's Study for Strings, the music ebbing and flowing amid the railway noise, and look across to platform 13, where the Jews once departed. I travel out of the city to the former Benedictine monastery at Breitenau, its Romanesque chapel turned into a PoW camp in the 1870 Franco-Prussian war. It later became a workhouse and prison for indigents and prostitutes, then a Gestapo-run camp for political prisoners and, following the war, a reformatory for women. Now it is a rehab clinic. From the 19th century until today, the local protestant church has been housed in the same building.

Breitenau, according to Documenta's artistic director Carolyn Christov-Bakargiev, is a palimpsest of all its earlier uses and a psycho-geographical locus for her project. She has a multiplicity of themes, including siege, hope, retreat and stage. All this takes some unravelling. Gunnar Richter's slide show documenting Breitenau is also on show in Karlsaue park.

"This variation, 2012," says a voice in a pitch-black room. It's part of Tino Sehgal's magnificent performance piece behind a decaying Huguenot house. Performers stamp and sing, whisper, holler and dance. They go through little routines as I stumble between them. Sehgal's exhilarating This Variation is among the best things in Documenta, as is choreographer Jérôme Bel's Disabled Theatre, a confrontational performance made in collaboration with actors with learning difficulties. Both Bel's and Sehgal's work concern presence and presentness, what it means to be a spectator.

Making sense of the world, let alone art or even yourself, is an unending process. We are bound to miss our step. Curating is essentially a matter of choices, the juxtaposition of work against work, artist against artist, place against place. The best exhibitions generate their own kind of sense. Christov-Bakargiev's skills are largely intuitive. She's feeling her way, as must we. She doesn't tell us what to think and has made a generous, full-blooded Documenta that touches many nerves.