Driving north out of Samawa towards Baghdad, a short way beyond the Euphrates bridge, a tarmac track leaves the main road, heading eastwards into a scarred, dun-coloured wasteland. Soon you enter the real desert, swept by sandstorms. Then, after 60km or so, a haunting scene unfolds.

Looming out of the haze, the eye begins to make out a low range of brown hills, at first shapeless, then taking form: the eroded stumps of ziggurats to the Goddess Ishtar and Anu ("Lord Sky"). This is Warka, a site few places on earth can match for sheer atmosphere, and a landmark in the human story.

William Loftus, the first outsider in modern times to see these sights in 1849, was almost overwhelmed: "I know of nothing more exciting or impressive than the first sight of one of these Chaldaean piles, looming in solitary grandeur from the surrounding plains and marshes ... Of all the desolate sites I ever beheld, that of Warka incomparably surpasses all".

4,000 years of history

Named Uruk by the Akkadians, Unug by the Sumerians, Erech in the Bible and Orchoe by the Greeks, the city was founded in the fifth millennium BC and survived into the first millennium AD. It was ruled in later times by Romans, Persians and Muslim Arabs before in the seventh century AD it was abandoned, except for the Bedouin, whose black tents still hug the horizon. To what extent Uruk really was the "mother of cities" is still hotly argued by archaeologists. It is claimed to be the birthplace of writing, mathematics and literature, and few would dispute that it is one of the most potent memory places of humanity.

The size of the site is testimony to the scale of the achievement of Mesopotamia, the world's first civilisation. Inside its silted gates, poking out of huge dunes, it is 3km wide and the circuit, dating back to around 3000BC, is 9km. Where the past century of archaeology has exposed them, you see great platforms and revetments of burned brick like the foundations of small skyscrapers. In places below the visitor's feet are strata 75 feet deep, which contain the shattered bric-a-brac of human history: Islamic glass, Hellenistic bowls, Parthanian clay coffins, greenish black-patterned Ubaid sherds and the little clay sickles used by the first dwellers in the Mesopotamian plain around 5000BC. In this one place is the image of civilisation: its rise, growth, triumphs – and perhaps its end too.

Like the cultures of the Nile or the Indus, Mesopotamia, as its name suggests ("the land between the rivers") owed its existence to a river system. Large-scale human societies had begun to grow from about 10,000BC in an arc through Syria, Palestine, Anatolia and the Zagros mountains. Starting with the first larger scale settlements at Jericho and Catal Huyuk in Anatolia, these were well built but still relatively small. It was only when sophisticated irrigation techniques were developed that the plain of southern Iraq was opened up to sustain a huge concentration of people and resources. Yet even this was still a relatively confined area: Mesopotamia had 25,000 sq km of irrigated land – similar in size to early dynastic Egypt.

From the fourth millennium BC came the first large cities, then states, whose culture and society would influence every aspect of life across west Asia – and further afield. In the third millennium BC, there were around 40 cities in Sumer and Akkad that made up the Babylonian plain. One big city-state, Lagash (whose site is more than 3km across), had 36,000 male adults in the third millennium BC, suggesting upwards of 100,000 people altogether. Uruk was probably of similar size. Each controlled an extensive territory: at Nippur, for example, 200 subsidiary villages clustered around five main canals and 60 smaller ones, joined by a web of countless small irrigation ditches – all subject to laws, customs and close control. These urban developments were fed by a trading network which, in the case of Uruk, linked Anatolia, Syria and the Zagros. Recent research has shown that Mesopotamia might not only have given birth to the world's first trading culture, but also the earliest private treaty stock market.

It is not surprising then that writing, written law, contract law, and international treaties are all found for the first time in the area. Not only does history begin at Sumer, but so does economics.

Art and war

View from Below of a Sculpture of Gudea, a Sumerian Ruler Photograph: © Macduff Everton/CORBIS

So who were the people who made this breakthrough in human history? The Sumerians were the prehistoric population of the southern plain of Iraq. Their ethnic and linguistic affiliations are not yet clear; their language is not related to any known language, though there are many theories. During the third millennium BC a close cultural symbiosis took place between the Sumerians and the Akkadians, who lived in the middle of the plain – the area around and south of modern Baghdad. Many of the civilisational achievements of Mesopotamia are the product of that symbiosis. Sumerian itself, though, had died out as a living language by around 1600BC, leaving it only the preserve of Babylonian scientists, scholars and liturgists. By the time the last Sumerian texts were copied in cuneiform in the Hellenistic age of the second century BC, the language had long been superseded by Akkadian as the language of literature in Mesopotamia. And the Sumerians themselves had long disappeared into the multiracial mix that was ancient Iraq.

In the 1850s, when the first major excavations were conducted in Iraq, it was still commonly held that the cultural progenitors of western civilisation were the classical world of Greece and Rome and Judaeo-Christian religion. Though the Book of Genesis mentioned Uruk, Akkad and Babylon, it was never suspected that these much older civilisations had had a profound influence on the civilisations of the Near East and the Mediterranean world. At that time it was also not known that Mesopotamia had led the way in the invention of writing and literature; in mathematics, science, astronomy and geometry; in the invention of the wheel; and in the earliest law codes. Even today, when we count time and space in multiples of 12 and 60, we do so because of the Mesopotamians.

Creativity and conflict

But if Mesopotamia was a place of cultural and technological innovation, it was also the site of constant conflict. With no natural boundaries, and no protection from neighbours, it was always open to attack from nomads and outside invaders, and internally prey to continual disputes over resources – especially water. Not surprisingly, then, this is where organised law appears for the first time in history – as well as organised warfare.

The history of Mesopotamia was then both uniquely creative and uniquely violent and destructive; marked by invasions and devastating wars in which the great achievements of its civilisation were smashed many times, from the ruin of the Ur III dynasty through Mongols, Tartars and Seljuks, to the savagery of recent wars.

Nevertheless, a single civilisation survived through all these conflicts – one that is recognisably Iraqi: a land of "singular destiny" as the French historian Fernand Braudel put it. The character that emerges is very different from the optimism of Egyptian culture. Early Iraq was pessimistic in its view of human destiny – its poets knew the achievements of humanity were fragile and always fated to be wiped away. This insight informs the world's earliest literature and comes right down to the rich vein of modern Iraqi poetry. It perhaps also explains why lamentation became a ritual tradition in ancient Iraq and still is in Iraqi Shiism; a cultural personality that is still part of the way Iraqis are seen by other Arabs.

How and when did ancient Iraq end? One should note that in Iraqi culture there is no clear dividing line between the ancient world and the medieval. Alexander's conquest in 331BC might look like an ending on paper, but in fact it inaugurated Uruk's greatest age during a thousand years of multilingual Hellenic culture in a vast region stretching as far as India.

The Arab conquest of Mesopotamia in the seventh century AD looks like another cultural turning point, but even then, change was slow, with a more immediate impact on mentalities rather than material culture and custom. Just as Christianity inherited the Roman empire in the West, Islam inherited West Asia and the Near East; and in this sense Islam could be seen simply as a continuation of the much older culture that underlay it. Baghdad, the great capital of the caliphate founded in AD762, was still a vast Mesopotamian city, made of burnt brick in the ancient way. And if change was slow in Baghdad, it was even slower in the old cities. The sacred city of Nippur, for example, continued to be a provincial centre for scholars – Christian, Jewish and Muslim. It was a crumbling old Iraqi town, with its warren of alleys like today's Irbil or old Kirkuk, with mosques, churches and synagogues, its sufis and its Talmudic lawyers. Out in the countryside the old Mesopotamian religion survived until cAD1000, among pagan tribes in the south of the plain who worshipped the deities of the primal waters, the abode of the old Sumerian god Enki.

In Iraq, the real dividing line between the ancient and modern worlds was the Mongol invasion of 1258, when the country's vast irrigation works were ruined and the population decimated. But even then the ancient world never really ended. Even today, in the streets of Najaf during the Shia ceremony of Ashura, people still enact the communal ritual lament, which was so striking a feature of their ancient culture. Even in their traditional clothes one might see a link: Herodotus' description of typical Babylonian clothes – keffiya jalabiya and dishdash – can be seen anywhere today.

Another intriguing aspect of Mesopotamia's cultural influence is its impact on western and Arab literature. The rediscovery of its ancient literature in the 19th century stressed links with the Bible: stories of the Flood, Noah, the Tower of Babel or the Garden of Eden were all tales that far predated the Old Testament. Ezekiel's Babylonian vision of "the likeness and glory of God" is thoroughly Mesopotamian. But scholars have been far slower to cotton on to the fact that later Arabic and Greek literature is permeated by Mesopotamian ideas, images and stories. Especially influential was the cycle of tales about the legendary king of Uruk, Gilgamesh, which might just be the single most influential work of literature in the world. It is now clear, for example, that many of the Tales of the Arabian Nights are transformations of ancient tales that had long circulated orally. The same goes for Gilgamesh's great quest for the secret of eternal life, a journey of the soul that percolated into medieval Islamic mystical tales and even, it seems, into Dante's Inferno. Early Greek literature – especially Homer, Hesiod and the early epic tradition – was strongly influenced in form and content by Gilgamesh. Mesopotamian civilisation, in short, is still alive in the ways we think, count time and measure the world, but also in the stories that we love most.

Saddam's Mesopotamia

A US army helicopter flies over the stepped Ziggurat temple, a three-tiered edifice dating back to 2113 BC Photograph: ESSAM AL-SUDANI/AFP/Getty Images

In the age of Saddam, the history of Mesopotamia was co-opted by the Baathists: massive restoration projects were undertaken, some impressive (such as the ziggurat at Ur), some megalomaniacal (such as rebuilding the palace at Babylon with Saddam's name stamped on to every 12th brick). Travellers in Iraq were confronted by huge murals and billboards of Saddam at Ur: Saddam on the white horse of Hussein at Karbala; Saddam receiving the Tablets of Destiny from Ashurnasipal himself. But the wars of 1991 and 2003 have left the country's incomparable heritage wrecked.

Previous generations, of course, had seen many of Iraq's treasures taken to London, Paris and Berlin. But what is left has suffered grave damage. Great sites such as Uruk and Nippur survived, but Babylon was badly damaged, and isolated sites have been systematically looted – Umma, one of the world's earliest cities, is now pockmarked by illicit diggers' pits; clay tablets from temple libraries have appeared on the art market. Iraq's National Library was also damaged, and many modern archives are reported destroyed.

Like the other great civilisations – Greek, Indian, Chinese, Persian – Iraq had the ability to remake itself over millennia, preserving its own distinctive vision. The author of the epic of Gilgamesh asks us to "walk the walls of Uruk … what human could ever equal them? Go up, go on; walk around – look at the foundations. Are they not magnificent? Didn't the Seven Sages themselves lay it all out?" His admiration of the achievements of humankind is all the more poignant as we walk around Uruk today under the contrails of allied jets amid the destruction of our time.

Michael Wood is a film-maker and broadcaster who first worked in Iraq more than 20 years ago. His latest book, The Story of England, is published by Viking