W G Sebald's narratives are both old and new, in form and subject matter. They are characteristically modern in that they attempt, more and more desperately and elaborately, to make sense of a world that is always elusive. His isolated narrators move through a world with none of the ancient structures of thought and feeling - no myth, no pattern of belief - trying to make sense, and also afraid of making sense.

They move through both time and space, making endless connections. In time, they explore the structures of memory, private and public. There are digressions on national, local and individual history. People burrow through archives or examine diaries. Sebald uses public and private photographs and snapshots to telling effect - frozen moments of human or geological or national time that are both present and absent. His characters study traces of human and animal predecessors long gone. Like many modern artists, visual and literary, he is interested in collections and catalogues - birds and insects, fish and stones.

His steady-paced narrator, a witness who is subject to fainting fits, vertigo and loss of consciousness, encounters others for whose narrations he is the audience. They make connections, geographical and imaginative. They are wanderers on foot and also on the railways, those iron lines with junctions and vanishing points which have unified Europe and carried armies and cattle trucks and condemned men, as well as commerce and tourists. His people are interested in human constructions of order - architecture, ancient and modern, factories, working and ruined, fortresses and concentration camps. They move with mournful curiosity through museums and churches and galleries. Everything is interesting, even the most solid things are evanescent, everything is full of dangerous meanings and secrets, as well as lost paradise.

The form is an old form, in that it harks back to what Northrop Frye called the "encyclopaedic" literary work. In The Rings of Saturn, Sebald frequently invokes Sir Thomas Browne's Urne-Buriall, with its coiling sentences enfolding many pasts and many reflections. He also resembles Richard Burton. His work is a modern Anatomy of Melancholy. But the way in which he exploits the ranging forms of memory is very modern, partly in the particular sense of being post-Freudian. His edifices might be said to be constructed out of random free associations - "think of whatever comes into your head". Sebald's wandering observations, quotations, photo-flash memories have at the same time the randomness of "free association" and the sense of the hidden form of rigorous and ineluctable destiny. Nietzsche said the reality of pure chance was the new form of fate, and a life, and history, do have discernible shapes in a world of chance.

That is not the whole story, because Sebald uses his method to explore the simultaneous memory and forgetting of modern Germany. Both his German characters and his many Jewish or part-Jewish characters have a double need to connect, and not to connect, to forget. Both have had their memories, cultural and personal, taken from them and made terrible. The wandering Jews of The Emigrants are slowly driven to suicide - in many cases, by a slow etiolation of their sense of self, cut off from all its roots and origins, suppressing intolerable griefs and memories. The Jewish Manchester-based painter Max Ferber, in the wonderful last section of that book, comments: "When I think of Germany it feels as if there were some kind of insanity lodged in my head. Probably the reason why I have never been to Germany again is that I am afraid to find that this insanity really exists. To me you see, Germany is a country frozen in the past, destroyed, a curious extraterritorial place, inhabited by people whose faces are both lovely and dreadful. All of them are dressed in the style of the Thirties, or even earlier fashions . . ."

The German narrator of Sebald's first book, Schwindel, Gefuhle (Vertigo), is equally reluctant to revisit Germany or his birthplace, though he eventually does so. Sebald's wandering Jews have been severed from a Jewish and also a German culture they believed was theirs. The Germans feel that they are severed from their culture by what was made of it under the Third Reich. Much powerful modern German art is concerned with this severance, the sense that it is only permissible to work in vacancy, a new, uncontaminated beginning. But in both cases, the repressed past - including poems and paintings, thinkers and ancestors - rises up to haunt the solitary modern, giddy in a void.

Sebald's narrator in The Emigrants, studying Jewish graves in Kissingen and Steinach, remarks that his head and his nerves are affected by "the mental impoverishment and lack of memory that marked the Germans". He also remarks that "perhaps there is nothing the Germans begrudged the Jews so much as their beautiful names, so intimately bound up with the country they lived in and with its language". He gives a list of these, all names translatable into solid German objects, brooks, mountains, trees, gold-dust, woods, including names also belonging to great artists - Auerbach, Grunewald.

His new novel, Austerlitz, returns to these themes. It is the story of a man called Austerlitz, narrated in various railway stations and eating places to a vanishing listening-narrative voice. Austerlitz was a Jewish child, sent on a Kindertransport to Britain in 1939 and adopted by a Welsh Calvinist minister and his wife. The couple do not tell the child he is adopted; he discovers at school that his real name is Austerlitz. He grows up to be an architectural historian, orderly, impersonal, repressing all curiosity about his origins, until this makes him ill, with the familiar vanishing and giddy feelings. He then finds his roots in Prague, and tries to trace his mother's fate in the Jewish ghetto of TerezIn, or Theresienstadt.

Austerlitz's discovered name is simultaneously overdetermined and meaningless. It is a time and a place in history, where many were slaughtered in a great Napoleonic battle. It is a railway terminal in Paris, next to the magniloquent architecture of the new monumental Bibliotheque Nationale, where he researches TerezIn while looking for traces of his father, probably transported to the camps from Paris during the war. Sebald's art of connecting the disconnected appears when Austerlitz finds only three other people with his name. One is Fred Astaire, born Austerlitz, whose father came from Vienna and worked as a master brewer in Omaha, Nebraska. From his veranda, you could hear "freight trains being shunted back and forth". Astaire said that this sound, and the idea of long train journeys, were his only childhood memory. Then there was the rabbi who circumcised Kafka's nephew. (Sebald's books are all haunted by Kafka.) And a woman, Laura Austerlitz, who was a witness to a crime in Trieste in 1944 and made a statement about it in 1966.

Too many connections in an unthinkably interconnected world. And a central absence of unspeakable things. This is Sebald's extraordinary construction. I think he is one of the important writers of our time, in any language. Austerlitz is perhaps stiffer, less surprising than the earlier novels because it feels more overtly constructed, less inevitably and strangely discovered. But it is nevertheless full of moving things and happenings, retrieved from the debris of the past.

A S Byatt's latest book, On Histories and Stories, is now available in paperback (Vintage, £7.99)