Look carefully among the forest of matchstick-thin figures and you will find it. A single canvas painted in an almost monochrome palette of brick red and brown. The subject: an apple on a sideboard. The artist: Alberto Giacometti. Apple on a Sideboard is one of the most surprising and significant works in the first major show devoted to Giacometti in this country for over 30 years. Of course the painting is a visual metaphor for human isolation - a Cezannesque exercise in fruity symbolism. Yet it is much more than this. In this one image it is possible to discern the essence of one of the most complex and rewarding artists of the 20th century. Gaze at it for long enough and the apple appears to float above the sideboard - the picture itself dissolving into Giacometti's signature framework of layered and cross-hatched lines and brushstrokes, to leave only the ineluctable weightlessness of the apple.
In 1958, Giacometti, in conversation with Jean Genet, summed up this sensation: "One day, in my room, I was looking at a towel lying on a chair ... The towel was alone, so alone that I felt I could have removed the chair without the towel moving. It had its own space, its own weight, its own silence even. The world was light, light..."
The greatest triumph of this extraordinary show is to allow us to see how Giacometti gradually succeeded in achieving this autonomous lightness - the unbearable lightness of being - in all his work, but principally, and astonishingly, in sculptures made of a tangibly heavy metal.
Giacometti was a magus. A peerless prestidigitator, he imbues the pre- Classical, hieratic forms of his major bronzes with a disquieting levity. Giacometti's sculptures are not merely monumental presences in space, but the means of defining that space itself. In his hands, clay is worked to the point of near obliteration, to be cast in bronze and transformed in the process from the worldly into the ethereal.
Somewhere in your subconscious you will probably carry an image of what Giacometti means - an archetypal, improbably skeletal figure, thinner than the most anorexic super-model. You may too have some perception of an association with Sartre and the received interpretation of these sculptures as the physical equivalent of the tortured existentialist literature of post-war Paris. Neither will prepare you for the variety, vitality and sheer power evident in this exhibition.
Giacometti is one of the defining figures of our century. Born in Switzerland in 1901, the son of a successful painter, he showed a precocious talent from an early age. The youthful portrait studies on view here contain, in their blunt frontality, some hint of his future direction. Trained in Paris by Rodin's pupil Bourdelle, by the age of 24, Giacometti had already passed with some distinction through forms of Divisionism and Cubism and, via the influence of Africa and Brancusi, into a satisfying quasi-primitive style that echoes Epstein and Lipchitz. The first of two remarkable epiphanies came in 1929 with the discovery of Surrealism; the second only five years later in 1934 with the first experiments in a new figuration.
Like Giacometti's own progress, this show is not easy. Often, it is uncomfortably confrontational; from the watching eyes of the portraits to the unreturnable stare of Gazing Head, a barely articulated piece of flat, hammered bronze. At every turn the viewer is invited, expected, persuaded to become involved in a dialogue with these mute objects. In presenting them so skilfully, this exhibition reveals that, above all else, Giacometti is about the difficult experience of being human. In Three Walking Men (1948), for example, three figures cross over each other's paths. The artist defined them as "men in the street who come and go ... a bit like ants, each one going about his own business, alone, ignored by the others. They cross paths, pass by, without seeing each other, without looking." It is about the way in which we use space and implicitly about how hard it is to relate to our fellow human beings. Giacometti understood this. He wasn't good at relationships. For women he frequented the brothels of Paris, entering into the artificial, contractual relationship of client and professional. He told Genet: "When I'm out on the street and I see a whore with all her clothes on, I see a whore. When she is in my room and naked before me, I see a goddess." But on the evidence of his art, his reaction was hardly that of Lautrec. If Giacometti's woman is a goddess, she must surely be the vengeful Isis, rather than comely and accommodating Pomona.
Giacometti is a contradiction. Ever in search of the reality of the human condition, when eventually confronted by it he bolts, desperately eschewing the physical. His people, whether sculpted or painted, have a similar habit of dissolving. In 1939, the year in which he finally abandoned abstraction in favour of his now familiar style, Giacometti began to make sculptures only centimetres high. Invited by his architect brother Bruno to show in the centre of a Zurich pavilion, he turned up not with the expected monumental bronze, but with a single, tiny, two-centimetre-high figure of a man on a heavy plinth. (It was not exhibited.)
"To my terror," wrote the artist, "the sculptures became smaller and smaller ... their dimensions revolted me and, tirelessly, I began, again and again, to end, several months later, at the same point."
In fact, it was only through a gradual, and palpably painful process, lasting some eight years, that Giacometti's figures began to grow; rising up shoot-like from the earth, until by 1947 they had emerged fully liberated and necessarily, utterly exposed. Over the following 13 years, in Giacometti's hands they were refined and manipulated into the brittle vulnerability of Woman of Venice. It is the starkness of the relationship of such sculptures as this to the space which surrounds them that lies at the heart of Giacometti's art.
A preoccupation with defining the indefinable had been evident as early as 1934 in the extraordinary sculpture Hands Holding the Void. The form is ostensibly inspired by a First World War gas mask found in a flea market, tempered with borrowings from the primitive. The substance of the work, though, is distilled into the few centimetres between the hands - a crucible of emotional tension that points directly to the mature work of the late 1940s. Two pieces here epitomise this growing obsession. The Hand, dating from 1947, a disembodied limb on to which we must project our own imaginings of a personality, is the natural development from a classic Surrealist drawing made by Giacometti in 1933. In Le Table Surrealiste the viewer instinctively fills in the blanks between a dummy head, an anatomical hand and the table on which they rest, to create the fleeting impression of the figure of a young girl. Look, too, at Figure in a Box Between Two Houses of 1950, a claustrophobic vitrine in which a man (implicitly the artist) walks, bent-backed, between two mutually oppressive blocks of bronze. Mankind, observes Giacometti with some resignation, is always struggling to get somewhere, striving impotently towards some metaphorical or spiritual goal. By way of emphasis, his figures are encumbered by a disproportionate mass of matter at their feet, locking them inexorably into their own physicality.
The sculptures created by Alberto Giacometti between 1947 and 1960 are among the most powerful and accessible means at our disposal of understanding the frailty and irony of the human condition. This is one of the major exhibitions of the year, deserving of the sort of attention accorded the Tate's recent celebration of Cezanne. It is an unforgettable experience for which the National Galleries of Scotland deserve full credit. Do not miss it.
n Scottish National Gallery of Modern Art, Edinburgh (0131-556 8921), to 22 Sept. At the Royal Academy, London (0171-439 7438) from 9 Oct to 1 Jan 1997