Standing on top of a gigantic pinnacle of desiccated mud in northern Pakistan, I once tried to catch my first glimpse of the river Indus. There were, however, simply too many other pinnacles of desiccated mud between, a huge desert of vicious rain-ripped gulches and sun-baked rills. "When I was a boy," said an old villager who had accompanied me, "we walked down to the river through forests and often saw deer, even tigers, by the water's edge." He added grimly: "The river is dead now." At that moment I realised I was looking at a disaster of deforestation and drought, one that had occurred within living memory.

The Indus, it seems, is not the serene and unchanging waterway we would like it to be, but a troubled reflection of human problems. It is this turbulent history, entwined with a superlative travel narrative, that Alice Albinia takes as her subject: from the 4,500-year-old marvels of Mohenjo-daro to the bitter divisions of today. And a masterful study it is, if often a melancholic one, given the calamitous irrigation projects, the religious and ethnic rivalries, the sheer stupidity and ignorance that mean the river no longer even reaches the sea, but dies an ignominious death in the plains of Sindh.

Albinia is a determined and observant traveller with a rare ability to find the right person and listen to their story. As her journey upriver winds through the geographic and cultural landmarks, she illuminates the history with her observations, linking past and present with delicious insights and ironies. At Jhok, for example, a dusty village in Sindh, she visits the shrine of the 18th-century mystic and proto-socialist Shah Inayat, a man whose message of simple love and equality so alarmed the Mughals that they had him bumped off. His descendants have become part of the system detested by their revered ancestor, raking in the money with the help of 300 landless peasants. Faced by the doughty Albinia with this rather uncomfortable truth, the Guardian of the Shrine tells her: "Shah Inayat is alive. Whatever Shah Inayat is saying, I am saying. I am Shah Inayat," inadvertently revealing, as she says, the continuity of ancient notions of reincarnation. "Seemingly irreconcilable ideas," she writes, "merge by the simple osmotic process of being in close contact with each other."

She starts her journey in Karachi among the untouchable Bhangi caste, who still clean the city's sewers, their pariah status and unsavoury job untouched by the trumpets of freedom and democracy blown at independence in 1947. Among them she learns the human cost of Partition, an arbitrary and foolish line of division that took no account of social divisions, themselves reflections of the topographic realities drawn by the river. With the Indus and its tributaries divided between belligerent nations, there was little chance of enlightened management of water resources, and the result is that Karachi, once a clean city washed daily, is now a festering sore barely kept alive by its lowliest residents, the sewage cleaners.

Travelling upstream by boat, she soon learns how bad that management has been - the water runs out and she has to abandon ship and take to buses. In a delta that has shrunk from 3,500 sq km to 250, she meets the Sheedis, descendants of the slaves taken from Africa to Asia by early Muslim traders. Regarded by other Pakistanis as jungli (wild) and jahil (ignorant), the Sheedis have learned to be ashamed of their remarkable heritage. Albinia's dedicated rooting out of their story is almost thwarted when she finally meets the man who knows most, the son of "Musaffir" Muhammad Siddiq, who wrote the only accounts of Sheedi history. The son's collection of Musaffir's books, she discovers, has been largely destroyed in a cyclone and the local library's copies eaten by mice. On top of that, the son, Bazmi, has suffered a stroke and can no longer speak, read or write. By candlelight Albinia sits down with his daughter and translates what little remains, piecing together an astonishing family story.

Musaffir was born in 1879, the son of an 86-year-old Zanzibari, Bilal, whose entire family was wiped out in a tribal war in the 1790s. Following that disaster he was sold into slavery and shipped to Muscat, and ended up in Sindh working for a stonemason. This man proved to be a kindly soul, educating Bilal and finding him an African wife. Years later, after 29 dead infants, a son was born, Musaffir. Helped by a Hindu nobleman and inspired by American abolitionists, he went on to write the history of the Sheedis. That should have assured him a place in the hearts of the million-strong Sheedis, but the modern-day community care little for such things, preferring to disguise their origins.

Further upriver, she finds the forgotten tombs of the Kalkhoras, rulers of Sindh in the 18th century who resisted the emerging power of the East India Company. Frescoes in the tombs record the colourful panoply of former lives: the river full of fish, the trees laden with birds and fruit, the people busy with hunting and domestic tasks. Neither the Kalkhoras nor their estates remain; the tombs lie unprotected and are slowly disintegrating. "In Europe," she observes, "such treasure would sustain an entire tourist industry. Here, they stand in a windswept desert, blown by the sand, visited only by the occasional porcupine."

Any traveller would be proud to have found such lost monuments, but for Albinia it is merely the start of something. Some of the frescoes show scenes based on the songs of the 18th-century poet Shah Abdul Latif, and soon she is at the man's shrine, experiencing the raw energy and exhilaration of a three-day festival. Here all of Pakistan's richly varied traditional culture is represented, with Hindus, Shias and Sunnis peacefully celebrating side by side. Even the Sheedis appear, jumping up and down to their mugarman drum. Like other passages in Empires of the Indus, this one manages to convey a message of beauty and hope in all the desiccated wastes, both physical and metaphysical.

There is much more here besides: tough journeying through Pashtun lands hidden inside a burka, fascinating diversions along the trail of Alexander the Great and finally a punishing mountain trek as she approaches the source deep in Tibet. The truly great achievement of this wonderful book is to reveal, unflinchingly and with panache, the rich and varied heritage of the Indus in all its appalling splendour.

· Kevin Rushby's Paradise: A History of the Idea That Rules the World is published by Robinson.