In 1971, the Italian artist Alighiero Boetti set foot on Afghan soil for the first time. It was the culmination of his growing fascination with faraway cultures and how they could participate in his work. Perhaps Boetti didn't intend his trip to be anything other than a fulfilment of a hippie wanderlust; but it became the beginning of a lifelong love affair with the country, shaping much of his best-known work - in particular the Mappa, his series of large, intricately woven maps. Boetti opened, and stayed regularly in, a small hotel in Kabul, which he named the One Hotel, a base from which he planned many of his works and did business - via middlemen - with the craftswomen whose identities would become so interwoven with Boetti's own.

In the extensive retrospective of Boetti at the Reina Sofía in Madrid - occupying an entire floor of the grand former hospital, if anything it's little too vast - these maps are pivotal. But Boetti's origins as an artist lie in the Italian arte povera movement and his subsequent rejection of it. Early pieces show a characteristic playfulness and humour as well as the use of lowly, workaday materials. Informed by his industrial home town, Turin, where he was born in 1940, he creates pieces that become far more than a sum of their simple parts: a cylindrical tower that's made of rolled-up cardboard but looks like turned wood; a metal cube containing zigzagging shelves of stripy municipal deckchair fabric; grouped-together bundles of coloured kindling wood or plastic tubing; and Colonna (1968), a striated classical column that looks like it's hewn from rough marble but is made up of thousands of glued-together paper doilies - a single-finger salute at the hushed world of Italian design.

In 1969, Boetti rejected the arte povera label and became interested in exploring his identity, reconfiguring himself as the twins Alighiero e Boetti (Alighiero and Boetti). Much of his work from this period reimagines the self-portrait - two brass commemorative plaques display the dates 2040 (100 years after his birth) and 2023 (poignantly, the projected year of his death: he died in 1994). Surprising in their delicate beauty are his 1969 self-portrait Xeroxes: his face a faint image on the paper, hands spelling out the title, Autoritratto, these ghostly images seem to owe something to the celebrated shroud of Boetti's birthplace.

Subsequent rooms are arranged thematically, much of the work reflecting Boetti's interest in travel and war zones. In the time-honoured tradition of the artist's atelier, he explores the concept of the artist as conceiver but not ultimate creator, giving clear instructions to craftspeople or artists - whether weaving women in Kabul or anonymous jobbing student artists. He creates ordered, intricate patterns only to revel in these patterns being broken, either intentionally or by miscommunication.

His 1980s Order and Disorder pieces are great examples of both this chaos within pattern and his forays into Afghan craft. Made of multicoloured squares of embroidery, each letter is picked out in a different colour chosen by the weaver. Every now and again, the colour of thread will have run out or a spelling mistake has been made. While meticulous in his instructions, once out of his hands it seems Boetti loved surrendering his work to chance and error, the fallibility of the weaver intrinsically important to the final piece.

To my mind the most wonderful room contains Boetti's biro works, including Putting the World into the World (1973-75) and The Six Senses (1974-75) - and the humble ballpoint pen is not what first springs to mind on entering. Hung on all four walls of a large room in Reina Sofía, these are huge expanses of deep, rich blues and greens with gradations and patterns within them. They recall a stormy ocean or an inky night sky and are punctuated - literally - by white commas, which encode signature Boetti words. They also have a tapestry-like appearance. In fact, they're sheets of minutely scrawled coloured biro: each section executed to a set of instructions by a nameless student whose fingerprints are all over it. Each one is different but all are unified by Boetti's vision.

In a work from another series, entitled Aerei, Boetti takes children's book drawings of many different types of plane and scatters them on blue-ink backgrounds. They are skies crammed full of aircraft - multiplying like viruses, showing order and chaos, speed and stillness, at once exhilarating and terrifying - a boundless world above ground in contrast to his ordered world maps below.

So back to Afghanistan and the Mappa pieces. Each one depicts a map of the world; each country consists of its respective national flag woven across it. Boetti would prepare the templates in Italy using up-to-date borders and flags but everything from thereon in was in the hands of the Afghan weavers and each piece would take up to five years to complete. They are exquisite pieces of craftsmanship and collaborative art as well as a geopolitical documentary of the changing world order from the middle of the cold war until the fall of communism. In the final map, the red Soviet bloc is suddenly peeled away to reveal many different new nations. Most remarkable is the colour of the sea. In most pieces, the weavers have rendered the oceanic expanse in hues of blue but now and again there is green, even pink. Living in a landlocked country, these were women who had perhaps never seen the sea; their choice of thread colour is both utterly pragmatic and wonderfully unruly.

“Alighiero Boetti: Game Plan" is at Tate Modern until 27 May 2012