Of the great triumvirate of Indian cities, Mumbai and Delhi are still centres of power and commerce, but Calcutta, or Kolkata as it now calls itself, has slipped from sight, a shadow of its former self. Except that it is still there, home to some four and a half million people. Amit Chaudhuri was one of them, but hesitated for three years before agreeing to write this book. It was worth the wait.

Chaudhuri has several strings to his bow. He is the author of award-winning novels, poems and essays. He performs crossover music and is professor of contemporary literature at the University of East Anglia, where he teaches creative writing. (I should declare an interest here, being a graduate of the course, although long before Chaudhuri arrived.)

One of the comments I remember from the late Malcolm Bradbury, who created the UEA writing course, was that if a reader reached page 27 of a book, they would be likely to continue. If I had not been reviewing this book, I might not have read that far because the opening pages show an unexpected lack of narrative muscle. Or perhaps the muscle is driving a narrative that is simply very discursive. Had I stopped early on, it would have been my loss.

Chaudhuri calls the 19th-century Bengali poet Bankim Chandra Chatterjee "the poet of what's at hand". The label could be applied to the author of the opening sections of this book. He is the collector of what's at hand as he tells us about his father living in the city, about how he buys a window from a derelict house, walks us along Park and Free School Streets, chats to stallholders, squatters, watchmen and so on. It is slightly rambling. (Later, I read that Chaudhuri wrote the book in real time, as he was living through the experiences he recorded.) And yet, by chapter three, page 71 to be precise, I was so immersed in the world Chaudhuri has created that I was surprised, when I looked up, to find that I was still in London and not among the crumbling mansions of what had been one of the empire's greatest cities.

This surprising book works for many reasons. One of them is Chaudhuri's style. He writes with familiarity, as though talking to us, knowing us, urging us to walk down here, to take a look over there. On some of the slower passages, I was half expecting him to lean over and discreetly urge me to keep up. His seductively simple style (no doubt achieved through endless drafts, for Chaudhuri tells us that he wrote the first draft longhand, on paper) comes into its own when describing character, as here: "Mrs Mukherjee sat upon her chair in the ground-floor flat in Lower Circular Road, almost meditating, except for the wicked, abstracted look the squint gave her, and the inward smile. She ruled the tea from the margins." Mrs Mukherjee could be a great creation, a central character in a different book, yet here she is just one of many who makes a brief appearance. How could one not now long for more?

Another reason Chaudhuri's book works is that his subject is so fascinating. Or perhaps we should call them his subjects, as he refers to the many moods and periods of the place, its "modern and ancestral and fabular" incarnations. There is the Calcutta of the Raj with its clubs where they still serve turkey at Christmas; the place of several villages that existed before the East India Company man, Job Charnock, chose them for his new base; the modern city, "born with the aura of inherited decay and life"; and the contemporary city, the forlorn city, that was being left behind in India's surge for progress. There are moments when he loses me, as when he draws parallels between Norwich and Calcutta. But there are many more where he wins me over, none more so than when he writes about his parents.

The range of angles from which he approaches these places gives the book great depth. The historical, the haphazard, the literary and intellectual  and the personal, for this is where his parents live and his father is fading. "Bombay is about money; Delhi about power; Calcutta is about parents", and not just for himself, as he introduces characters who have given up sparkling careers in other, more important cities, to be near ageing parents. The political is particularly well-handled; we are not traipsed through the hustings, but given several moments in the author's life in Calcutta when politics intruded, from the days of leftist rule to the rise of Mamata Banerjee and her Trinamool Congress party.

Out of this wealth of material and privileged access, Chaudhuri's Calcutta comes across as a city with "a stupendous disregard for norms and regulations", a place where "life and the imagination would hover most palpably over decay and dereliction". Chaudhuri's Calcutta has a different scope and intention to Suketu Mehta's Maximum City (about Mumbai) and to William Dalrymple's City of Djinns (about Delhi), but like those books, it succeeds brilliantly in making sense of a place few of us can know.