Gerhard Richter scales the heights

Tate Modern is fearfully pleased to be launching a major touring retrospective of the German contemporary artist, Gerhard Richter.

And so it should be. Now approaching 80, Richter is one of the true giants of the European painting scene, an artist who perhaps more than any other has tried to test and prove the value of painting in the modern age: painting over photographs, trying to find the overlap between the abstract and figurative, making it a medium of political commentary and constantly testing painting's limits in form, texture and possibility. Indeed, to some critics he has appeared as the most important painter of today. And if that appears a bit too hyperbolic, then at least it could be said of Richter that he is the European artist most able to challenge the pre-eminence of his American contemporaries.

Not that he shares the same culture, for all his devotion to the United States. Where American art is bursting, buoyant and above all emphatic, Richter's has always been an exercise in the contradictions, the ambiguities and the doubts about what art can and cannot do in an age of fragmentation and uncertainty. It's partly his background, of course. Born in Dresden in 1932, Richter, who claims to remember the Dresden bombing during the war, studied art at the Dresden Academy of Arts under the communists before moving to Düsseldorf in West Germany a few months before the building of the Berlin wall.

He first came to notice – and in some ways it is the work for which he is still best known – for taking photographs and reworking them as paintings. The Sixties in which he started as a full-time artist was the era of Pop art and popular imagery. Richter, who had received his first technical training in Dresden as an advertising and stage-set painter, took up the baton with the ironically named Capitalist Realism movement (no country has created quite as many art movements as Germany), a play on Socialist Realism. But in the hands of this East European it was used less as a political statement than a form of experimentation into what painting could do which photography and new technology of themselves could not.

From early on, and since, he has continuously tried to extend the limits of an idea, projecting a photograph on to canvas, repainting it and even re-photographing it again, or, as he later developed his ideas, photographing a painting, or a minute part of it, and magnifying it to the point at which it becomes a work of art in itself. In other hands it might have appeared just fanciful. In Richter's brush it becomes a means of lifting and changing the original image, to give it movement or confusion and ambiguity, and eliding the figurative with the abstract.

Early on there is real bite as the young artist faces up to the past as well as the division of his country. A picture of his father with a cat makes a mockery of the old man (who ceased communication with his son after he departed for the West) by exaggerating the hair and facial features. The macabre is again used, but this time with much greater sensitivity, in a portrait of his aunt Marianne, a depressive eliminated by the Nazis as mentally defective, while a standing photograph of his uncle Rudi, a Nazi war hero, is reworked against a grim backdrop of wall and barracks-type building to suggest war crimes and the pose of a man ready to be shot.

Later on, as well as doing sea, sky and landscapes using the same techniques, he takes pictures of bombed-out cities repainted in garish grey to represent the destruction of war, just as more recently he has reprinted aerial shots from Allied bombers of German cities to show the gap between the view from above and the havoc that will be wreaked below: the limits of photography against the imaginative leap that can be given it by painting.

The use of the still image repainted in black and white is developed with greatest effect in the series he did in the late Eighties of the arrests and deaths in prison of the Baader-Meinhof group. The Tate would have these as some of the most profound artistic political comments of the post war. They are certainly powerful, the images pinioned by paint to considerable emotional effect. And yet it is hard to see Richter as a great political commentator in the way of Goya or Picasso. You can see in the painting Richter did of 9/11, September of 2005. It's from a photograph of the World Trade Centre as the attacks occurred, but without the fireball dramatics most often portrayed. Eschewing the obvious, it is a work of great sympathy, with the grey and brown smeared across the upright building and the blue of the sky, but not of great moment. But then, while good art should reflect its times, it does not need to directly comment on them to be great.

The most dramatic moment in this show comes not with the representational but with the sudden explosion of colour abstract in the early 1980s. Richter had pursued the abstract through the single colour grey for some time before, describing the colour, typically, as the "welcome and only possible equivalent of indifference, non-commitment, absence of opinion, absence of shape." The statement is a tease. In fact, his exploration of grey is study in shape through texture and commitment through the manipulation of that texture by brush and scraper.

He had also been influenced by the Pop art of the time to take an interest in colour in the Seventies, through taking colour paint charts and developing the basic primary colours and grey into a hundred different shades randomly arranged. But then at the beginning of the Eighties he exploded in a burst of large-scale abstracts that played paint and colour in a galaxy of technique and juxtaposition. The Tate has a room of works from the period that at first shocks, then intrigues and finally seduces. And it is these abstracts, becoming more monumental in the succeeding years, their surfaces wiped by a "squeegee" that scrapes off layers, leaving smears, which provide some of the most exciting works in the show. Deploying not just different palettes – white being one of the most imaginative – but also different bases in aluminium and "aludiboard", Richter builds up layers of paint only to partially destroy them by scraping and even cutting the canvas.

The exhibition climaxes in six of the Cage paintings he made in 2006/7 while listening to the music of John Cage. They are masterpieces of the majestic, layered works in which almost every technique from the brush to the scraper is used to give them rhythm. Like the electronic notation of sounds they move across the canvas in blurred and random lines. The Tate is fortunate to have them on long-term loan. They should be exhibited alongside its Mark Rothkos, contrasting studies in abstract projection, the one of colour, the other of surface.

The Tate calls the exhibition – which has been jointly staged with the Centre Pompidou in Paris and the Staatliche Museum in Berlin – a Panorama, which is what it is, a synoptic view of the man and his work through his various themes and stages. What it covers is most of his history, what it misses is the way in which he has pursued his images through dozens and occasionally hundreds of variations. It illustrates the development, but not the obsessive way in which Richter likes to take an idea and then chase it through every possible avenue. Like the aerial view of Cologne prior to the bombing, it gives the picture but not necessarily the actuality. By any standard, Richter is a major contemporary artist. You can see how in this impressive show but not completely why.

Gerhard Richter: Panorama, Tate Modern, London SE1 (020 7887 8888) to 8 January