Julius is an American psychiatrist training in Manhattan. Of German and Nigerian extraction, he is rootless in New York. Entranced by the city, he is anxious not to fetishise his outsider status. He is also on the rebound from a relationship. These states of mind connect with walks that he makes across the urban grid, now for a purpose, now aimlessly.

Along with seemingly profound reflections on cultural forms, descriptions of these walks constitute most of Open City, the first full-length novel by Teju Cole, which has been much praised in the United States for its prose style and for its take on the city as a site of power, desire and community. It is akin to one of those "spatial stories" identified by the philosopher Michel de Certeau in his book The Practice of Everyday Life.

Breaking through the anonymity of the crowd, Julius has encounters with strangers, acquaintances and friends. These include Moji, a woman he knew as a girl in Nigeria, but had forgotten, or chosen to forget. He remembers his time in the Nigerian Military School, goes to Brussels, has sex with a middle-aged Czech woman there, comes back, has a picnic, gets mugged.

Saving a climactic invasion from Julius's past, that's about it so far as action goes. But action is the wrong spoor by which to pursue this book. What comes strongest off it, instead, is a cosmopolitan range of reference. Moments of genuine narrative are most often the springboard for a jump into book chat, music trivia or historical disquisition.

This dangerous gamble pays off. The environment of which Open City is mostly mimetic is the hall of semiotic mirrors inside our heads, and the proliferating data now so easily accessed by our fingertips: twin arenas of information which, at once dazed and delighted, we struggle to connect both to everyday life and an overall interpretative code.

Dramatising this, Cole recommences a process of synthesis between two aspects of the novel which have long consorted and contested with each other: between (as Malcolm Bradbury once put it) "on the one hand, the novel's propensity toward realism, social documentation and interrelation with historical events and movements, and on the other  its propensity toward form, fictionality, and reflexive self-examination".

Cole further calls on at least three city walkers out of literary history: the "strolling spectator" type which has informed the novel from its earliest days; the Baudelairean flâneur which transferred into fictional prose with tales such as André Breton's Nadja (Julius's ex is called Nadège); and the roving "I" of European romantic modernism, which has found its most eloquent recent exponent in the work of WG Sebald.

Open City is also effective at dramatising the relationship between objective and subjective experience. In one fabulous scene, Julius is stranded on a fire escape, high on the edge of Carnegie Hall. It's night-time. He finds himself lost in relativity, plunged between the wailing of an ambulance "reaching me from seven floors below" and "starlight that was unreachable because my entire being was in a blind spot".

These are the limits of being open. The book's title comes from the declaration by defenders, in the event of imminent capture, that a city is "open" and the enemy can march in. Reading Open City, it is important to bear the title in mind, and not become impaled on fixed ideas about what kind of person Julius is. Otherwise one might assume that his contemplations should be taken at face value.

For as well as being an excellent novel about spatial relations (compare Tom McCarthy's equally satisfying Men in Space) and layers of urban history and immigrant experience, Open City is a novel about an intellectual show-off. And if what Moji says is true, he is something much worse.

Negative space (the space between forms or around utterances) is key. We are disposed to read Julius's reflections for their so-called content, whereas we do better to read them in relief, for what they say about him. This is the real juice. We have to work hard to get it, searching in the gaps for what Julius calls "a double story". At the same time, it's in the nature of language and experience that the totality will elude us.

Part of the delight of Cole's book is how it exploits refinement until Julius reveals himself as a poseur through intellectual over-reaching, disclosing an irony for which readers may not be prepared. One instance of this comes when Chinese musicians in a park remind him "of Li Po and Wang Wei, of Harry Partch's pitch-bending songs, and of Judith Weir's opera The Consolations of Scholarship".

How to read Open City is obliquely signalled by these pretentious pratfalls. In the notes of the trumpet of another Chinese band, Julius hears the "spiritual cousins of the offstage clarion in Mahler's Second Symphony". I'm not a musician, but I suspect that's twaddle. But when he hears, in the same tune, the "simple sincerity of songs I had last sung in the school yard of the Nigerian Military School", and is returned, trembling, to a state of childhood innocence, the observation has the force of something genuine. The little emotional space to which no one else in the city is likely to have access is much more important than the public-facing attitudes of the cultural dandy.

Giles Foden's Turbulence is published by Faber.

Critics on both sides of the pond are hailing Teju Cole's novel Open City as a startling, sparkling and original debut. They are only half right. It is a strikingly original work, shimmering with its author's luminous intelligence. But it is not his debut.

That honour belongs to Every Day is for the Thief, a novella about a young Nigerian man's return home to Lagos from New York. It appears to have escaped the attention of critics because it was published in 2007 by Cassava Republic, a small Nigerian company. Arguably the best book about contemporary Lagos published in the past decade, Every Day is for the Thief received enthusiastic reviews on its publication in Nigeria. "This," said cultural critic Molara Wood, "is how to write about Africa."

A tiny gem of a book, it is filled with acute and clear-sighted observations about Lagos, a city from which stories emerge from every direction. "Had John Updike been African," muses the narrator, "he would have won the Nobel prize long ago. Shillington, Pennsylvania simply did not measure up to his extravagant gifts."

One can only imagine what Updike would have made of the Lagos of power cuts, traffic congestion, armed robbers and other hustlers, but Cole's gifts more than measure up to the task before him. He presents a Lagos of eccentricities and of joyousness as well as shocking levels of callousness. Through Cole's eyes, we experience Lagos as a city that is at once a product of its history and captive to its present, swerving between optimism and uncertainty.

That the Lagos of Every Day is for the Thief is a more hopeful place than the New York of Open City is testimony to Cole's refusal to write to stereotype. The unnamed narrator of the first book, who finds himself back in America again, responds actively to the city around him: he is in turns amused, indignant and horrified by what he sees. He is underwhelmed by the blithe description in the national museum of the slave trade as an "obnoxious practice" and dismayed by a display of Nigerian leaders that "celebrates the worst of the butchers that ran the nation aground".

Julius, the narrator of Open City, is just as sensitive to the New York whose pavements he plods, but he is essentially cut off from all around him. Every Day is for the Thief brims with energy; Open City pulls you into Julius's isolation, compelling you to share his loneliness.

Julius has reason enough to be unhappy. In the final year of his psychiatry residency at Columbia Presbyterian, he has been going through something of a rough patch. The space around him is filled with the absence of two women: his estranged German mother (his Nigerian father is dead) and his girlfriend, who has left him (and New York) for San Francisco. He is also desperate for something to help him "escape the regimen of perfection and competence" imposed by his work, which "neither allowed improvisation nor tolerated mistakes". He takes to walking up and down the streets of New York, his ceaseless strolls "a reminder of freedom".

There is a brief interlude in Brussels, but it is on New York's pavements that he walks. And while he walks, he thinks. And thinks. Cole draws us deeper and deeper into his mind, which has an astonishing depth of knowledge. Narrator and author range over subjects as varied as the slave trade, the music of Mahler, the paintings of John Brewster, Anthony de Hooges, an early Dutch settler, Belgian politics, the Liberian civil war, the Hungarian photographer Martin Munkácsi, bedbugs, killer bees and whales. Cole writes beautifully, weaving Julius's reflections seamlessly into his narrative. The hypnotic quality of Julius's introspection is sometimes interrupted by a level of detail that feels a little Wikipediac, such as when he reflects on a "fifty-four-foot sperm whale that beached itself in the sandy shallows of Berckhey, near The Hague" and took "four days to die and, in that time and in the weeks afterward, had entered into the legend of a nation at the very beginning of its modern history".

There are few jarring passages like this, mercifully, but when they do appear, they have the effect of inducing in the reader a strong desire to shake Julius for being an insufferable know-all. For the most part, he wears his erudition lightly, using it to illuminate aspects of New York that are relevant to his state of mind.

Cole is not only a fine writer, he is also a photographer and an art historian. He gives the reader a view of New York through the lens of a photographer, evoking the famous analogy Christopher Isherwood made of himself as a camera "with its shutter open, quite passive, recording". As Cole is an art connoisseur, it is apposite to compare his book with the old masters that he has studied. Like a Vermeer, a De Hooch or a Bruegel, which can be viewed many times and never fail to delight, Open City is a book that can be read again and again, with each reading bringing the reward of further insights.

Cole has said in interviews that he will turn his attention back to Lagos for his next book, a nonfiction account of the city. It cannot come too soon.