I have a photograph from Iraqi Kurdistan that I sometimes hope might appear in my memoirs above the caption, "Birth of the Iraqi tourist industry." It shows two men, Kanan Mufti and Ken Herwehe, looking over the plain of Gaugamela, where, 2,336 years ago, Alexander won his third and decisive victory against Darius. Gaugamela, with its turreted elephants and scythed chariots, had always been one of my favorites among Alexander's battles. It was the first great clash of East and West in Mesopotamia. Kanan is head of antiquities in Iraq's Arbil governorate, and Lieutenant Colonel Herwehe was at the time one of the senior U.S.commanders in the region. I had introduced them at Herwehe's headquarters in Arbil, hoping that together we could find the site of the battle. Kanan provided 11 sources, ancient and modern, rolled up in scrolls or pressed flat in large folios, to help us. Herwehe contributed a large table and a U.S. military aviation ground escape map.

A couple of hours of gluey tarmac and jolting riverbeds and back roads took us to the base of the Jabal Maqlub, where Alexander had camped overlooking the huge plain Darius needed to accommodate his army of hundreds of thousands. Features described by the ancients - mountain passes, hill flanks, and the great plain - stood suddenly revealed before us, all in their proper places, as the Mesopotamian geography yielded its secrets like a dusty cuneiform. I wanted to visit the ridge from which Darius had lost an empire. But Herwehe said it looked like land mine country. "Saddam's officers were good at reading the terrain," he said. "War hasn't changed so much since Alexander's day."

In Iraqi Kurdistan, a region approximately the size of Scotland with about 4 million people, a cultural and historical legacy of global importance coexists with natural beauty and dicey politics. And if Iraq settles into some semblance of postwar peace and prosperity, the Kurdish north will be a traveler's first destination: this is already today the most orderly, temperate, and beautiful part of the country.

Kurds comprise between a quarter and a fifth of Iraq's population, and the estimated 25 million Kurds who live in Iraq, Iran, Syria, and Turkey form the world's largest stateless nation. Iraqi Kurdistan's high mountains provide some of the best sanctuaries and richest water resources in the Middle East, and that water sustains the best agriculture in Iraq. The Kurds are both blessed and cursed with a strong historical claim to Kirkuk - source of almost half of Iraq's oil exports.

The Kurds in Iraq have tasted freedom in the 14 years since the United States and the United Kingdom set up the no-fly zone to protect them from Saddam Hussein, and now scores of political parties and dozens of newspapers jostle for attention in Iraq's three northern provinces. Religion is a personal matter here, and it is an easy place to drink whiskey with novelists in a university garden, or to drink wine with a Chaldean priest.

Even after their strong showing in the January elections, Iraq's Kurds are not convinced that their Sunni and Shiite Arab countrymen can guarantee an arrangement that does not excessively abridge the freedoms they have enjoyed among their own Kurds. And there is no shortage of homegrown threats to the Kurds of Iraq: their own region is split into two administrations that fought as recently as 2001. Iraqi Kurdistan's uncertain future and fraught political present often seem no less eternally Kurdish than the region's snowy peaks, green valleys, and archaeological riches.

Iraq's history is everywhere in its people. The Medes who fought for Darius at Gaugamela were the forefathers of today's Kurds. In Iran, Kurds explained to me that the Medes and Persians had been united under the Achaemenid dynasty that ended at Gaugamela; that they had ties of kinship, language, and history with the Persians; and that Iran's Kurds are comfortable within the Persian state - where they have been for more than 4,000 years - as long as they are treated fairly. Kurds in Iraq, however, will quickly remind you that they have no such history with the Arabs, no sharing of origins or language, no millennia of living within the same borders.

Modern Kurdish history has been one of cyclical repression, revolution, and opportunity wasted in naïveté and internecine conflict. A variety of Kurdish princes launched dozens of revolts against Persian and Ottoman rule through the 19th century. When the British formed Iraq after World War I by combining the province of Mosul with the Arab provinces of Basra and Baghdad, the Kurds acquired new enemies. Through the 1920's, 30's, and 40's they fought the British, and from the 1950's until 1991 they fought the Iraqi state - first the monarchy, then the junta of generals, and then the Baath Party and Saddam Hussein.

Kanan grew up in the citadel of Arbil, the Iraqi Kurdish capital. Arbil sits 100 feet above a flat plain, and every inch of its height is accumulated human history: it is the oldest city on earth, 8,000 continuous years of civilization - dust on bone on refuse on old mud walls - piled high in the middle of a hot brown plain where the Land Between the Rivers meets the mountains. Kanan does not remember for exactly how many generations his family lived in the Arbil citadel, but he remembers that their courtyard houses, with fountains and stairs going up to timbered galleries, were sacked and burned three times under Saddam. Even after more than a decade of freedom for the Kurds, the sooty scars of destruction are there today among the weeds and abandoned porticoes. Saddam's cousin "Chemical Ali" Hassan al-Majid once told a brother of Kanan's that the Iraqi army and security services had killed more than 100,000 Kurds between the spring and autumn of 1988. Under Saddam, almost every single one of the country's 4,000-odd Kurdish villages was razed. Kurds were shot, strafed, bombed, gassed, and forced into concentration camp cities.

Iraqi Kurdistan's second city, Sulaymaniyah, is cool and green for this part of the world, at the start of foothills that climb to the mountain border with Iran. There is a pretty walk under mulberry trees, and a grassy park with wide rose borders where students pace barefoot, mouthing formulas and Kurdish poems during exam season. On the roof of an academic building, the university's late president installed a café that men are not allowed to visit without women. He hoped to break the cycle of separation whereby fathers and husbands leave their families at home and unmarried couples are afraid to be seen in public. Others in Sulaymaniyah boast of at least five or six places in town where young men sip Pepsis with girls in tight jeans. It is the only city in Iraq where this happens.

Despite the success of the Iraqi elections, unrest continues. But the history-rich Kurdish north offers a preview of better things to come.

On the way from Sulaymaniyah to the Barzan Valley, an area that has been a center of Kurdish insurrection since the 1920's, there is a café by the Great Zab river. Fried fish is served under the oak trees, and canaries and nightingales sing through the sound of rapids downstream. In the evening there is a smell of hay in the valleys. If you walk in the hills above, the descent is like powder-skiing, with the daisies and the white-topped, thigh-high thistles gently brushing your legs.

In Barzan I spoke to an old man who basks in the name Abdulsalam Sheikh Sulaiman Sheikh Abdulsalam Barzani. On an acre near the center of town, he tends shady rows of figs, pomegranates, almonds, and apples. Around his plot were others - less profuse, but rich. Farther away there were sheep and cattle in pastures. All around us were hills where mountain oaks, which once blanketed the landscape, were coming back to a country denuded by Saddam with fire and chemicals. With the trees, birds and deer and wolves are also returning.

I wanted to walk for weeks in those hills, where the oaks made a pattern like leopard skin on the gold grass. But the mayor of nearby Mergasur, whose grandfather was hanged by the Ottomans in 1914 and who lost 37 cousins to Saddam, had warned me not to go too far or too high, or to spend time in the hills at night. The PKK - one of the deadliest guerrilla groups in the Middle East, Kurdish-Marxists, whose main struggle is in Turkey - is active in the high Iraqi border country from Syria to Iran. Other Kurds, who live near their camps in those lush valleys ringed by snow, are scared of them. Looking out at his own village and over the Barzan Valley, Abdulsalam said to me in English: "You see this beautiful place, so green and rich, the farmers, the merchants, all so full of optimism - yet every individual has a tragedy. Mothers, brothers, sisters killed. Torture, refugees." Barzan had been razed in 1983. Eight thousand Barzani men disappeared in a single night. Abdulsalam lost two brothers, an uncle, cousins.

"So much promise, so much pain," he said, as he sat cross-legged on the dark earth under one of his apricot trees, waving an arm over the valley. "This is Kurdistan."