Hailed today as a revolutionary pioneer of 20th-century painting, Wassily Kandinsky was oddly hesitant about becoming an artist. Until the age of 30, he pursued an academic career in law and economics at Moscow University. From 1896, however, the combined impact of Monet's hay-stack paintings and Wagner's Lohengrin forced him to change direction. He left his native Russia and began all over again, studying art in Munich and falling in love with the talented young German painter Gabriele Münter.
He is already 40 by the time we enter the enthralling Tate Modern exhibition "Kandinsky: the path to abstraction". A man in a hurry, he threw himself into a decade filled with ceaseless experimentation. Travelling through Murnau, in the southern Bavarian Alps, he discovered an elemental world, studded with farmworkers' homes and foliage blazing fiercely against the dark mountain ranges beyond.
The landscape made him feel homesick for Russia, where he had relished the brilliant colours of painted icons and folk art in ancient wooden houses. A 1906 painting called Volga Song looks back to a remote past where heavily bearded travellers embark on an epic voyage in boats carved with images of wild animals. Yet there is nothing remotely traditional about Kandinsky's handling of paint. Excited by the "wild beast" movement in France, where Matisse and André Derain had led the Fauvist rebellion, he simplifies the Murnau landscape before bathing it in startlingly high-key colours.
Kandinsky, envying the freedom of the composer, tried to cast off art's heavy reliance on recognisable subjects. Inspired by his new Viennese friend Arnold Schoenberg, whose bold transformation of musical theory provided a parallel to avant-garde painting of the period, Kandinsky called his most ambitious paintings Improvisation or Composition. His subject matter became equally turbulent. Kandinsky was haunted by visions of the Last Judgement, in which avenging angels blow trumpets of doom capable of shattering everything in their path. The Bavarian mountains appear to tremble, and even Murnau's once-sturdy church seems on the edge of total collapse. But he did not view this Götterdämmerung with despair. Kandinsky's deeply felt and influential book Concerning the Spiritual in Art outlines his mystical belief that the sinful would be overcome by the sacred. He was convinced that the painter could be guided by the voice of "the invisible Moses", and he looked forward with confidence to a worldwide spiritual reawakening.
A 1911 photograph shows many religious images on the walls of Kandinsky's home in Munich, but in his own art he was determined to jettison overt references of this kind. In the same year he founded, with his equally adventurous friends Franz Marc and Alexej Jawlensky, the great expressionist movement called the Blue Rider. The image of a figure on a leaping horse surges across their Kandinsky-designed manifesto, The Blue Rider Almanac. It announces a desire to be liberated from the constraints of past art and to enter an undiscovered world where line and colour play far more emancipated roles.
Beside this feeling of exhilaration, however, Kandinsky's awareness of danger grows. Cossacks suddenly appear in one canvas, wielding immense weapons as if preparing themselves for battle in a world riven by upheaval. And a nightmarish painting called Improvisation 11 (1910) is dominated by a brilliant yellow sail, rising up as if in shock as hirsute patriarchs fire their rifles at boat passengers struggling to escape. Below the raised barrel of a battery gun, a dog bites its own leg. The dog's distress sums up the mood of this belligerent vision, in which self-destruction seems as likely as execution by firing squad.
By now, Kandinsky's infatuation with colour has reached an unmatched pitch of intensity. He seems to be intoxicated by the freewheeling language that he is inventing in his new work. But it never reaches the point of complete abstraction. Unlike Kasimir Malevich, who pushed avant-garde Russian art to a geometric extreme, Kandinsky could not resist including renegade hints of figures, flowers and mountains in his most audacious paintings. A trio of grotesque clowns emerges towards the top of one canvas, grinning as they ride out the storm. Composition VI (1913), by far and away the finest work on show at Tate Modern, is given over to a tumult of intergalactic forms, tumbling, twisting and thrusting as they find themselves caught up in an overwhelming frenzy. But even in this turmoil, a solitary fish, impaled on a spear, can be detected at the top of the immense canvas.
Writing in a revolutionary magazine aptly called The Storm, Kandinsky tried to argue that Composition VI was optimistic: "a great objective disaster in its independent meaning is as much of a eulogy as a hymn about the new birth that arises from it". Although Kandinsky was one of the first artists to prophesy the advent of military upheaval in 1914, he remained ambivalent about the effect of violence on and in his works.
Though he gave his powerful Improvisation 30 the subtitle Cannons, the smoke belching from their barrels spreads across a chaos of seismic, unrecognisable forms. Another turbulent work, pointedly called Fugue (1914), suggests that he still wanted his art to be as free as music. For Christmas 1913, Kandinsky sent a present to his first English patron, Michael Sadler. It was, Sadler thought, "explosive and ballistic in its design". But when he wrote to Kandinsky a year later, asking if this painting "had foreboded war", the artist replied: "Not this war, but I knew that a terrible struggle was going on in the spiritual sphere, and that made me paint the picture I sent you."
After spending the war years in Russia, where his initial enthusiasm for Lenin's revolution swiftly gave way to disillusion with Soviet ideas about art, Kandinsky returned to Germany. The Tate show ends in 1921, just before he took up his teaching post at the newly created Bauhaus, which would become legendary. Peace was undoubtedly a relief, and yet some crucial element of vitality goes out of the art in the final room. It is more orderly and decorative than before, and its playful allure lacks the risk-taking audacity that gives his pre-war work its irresis tible spirit of attack.
"Kandinsky: the path to abstraction (1908-1922)" is at Tate Modern, London SE1 (020 7887 8888) until 1 October