In Europe, it is what historians call the High Middle Ages. The Seventh Crusade is under way, as Christians again attempt to wrest Jerusalem from Islamic control. The Magna Carta has been signed in England.

In roughly the area we today call the Four Corners and to the south, several Native American cultures, including the Anasazi, are at or near their creative and population peaks.Around this pivotal year Lawrence W. Cheek and the editors and photographers of Arizona Highways have created the dream book for those fascinated by the pre-Columbian American Southwest. They call it "A.D. 1250."

On the Colorado Plateau, in 1250, "the Sinagua are dying off or scattering," Cheek writes, "while nearby the Anasazi are building breathtakingly dramatic pueblos in the sheltering natural alcoves of canyon walls. In the Chihuahuan desert south of the modern border with Mexico, another people is operating an astounding Meso-amer-ican-like trading center complete with high-rise adobe towers and municipal water and sewer systems never before seen in this land."

But drought, enemy attack, overpopulation and other factors still being studied and speculated about will relentlessly undermine their ways of life over the succeeding two centuries. These societies will essentially vanish, though traces can still be detected among the peoples living in portions of Arizona and New Mexico.

Cheek approaches his subject as a journalist, marshaling much of what science knows about these cultures, gone now for six centuries, and leavening it all by regularly admitting that we really know little, hypothesize a lot and always must guard against our "European cultural conditioning." The book, in a 10-by-13 format, brings together maps, illustrations and scores of color photographs. These range from spectacular two-page landscapes to lovely detail shots starkly presenting basketry, pottery, jewelry and effigies upon the ivory-white paper.

Simply put, "A.D. 1250" is as handsome as a book can be.

Cheek tells about the Sinagua, from a Spanish term for "without water," who lived in the Flagstaff region, a borderland between other thriving cultures; the Salado, who created beautiful polychrome pottery coveted both then and now; and the Mogollon, whose most ambitious creation was the trading community today called Casa Grandes in Mexico.

The Hohokam built ball courts and devised an intricate irrigation and canal system in the Salt River Valley, "the remnants of which were still visible in 1867 when a prospector named Jack Swilling rode into the valley and realized that this desert had once been farmed and could be again. With that idea, Phoenix was born."

And Cheek writes of the Anasazi, who built striking complexes in Chaco Canyon, Mesa Verde and hundreds of other places. The rooms were small and dark, and their residents had to stoop to enter through the low doorways. But "to the Anasazi, `indoors' was for food processing, storage, sleeping, occasionally for cooking and a refuge during bad weather. Their `living room' was the outdoors."

In addition to chapters upon each of the cultures, Cheek directs readers to specific sites around the Southwest. An accompanying travel guide and fold-out map further points the way. The emphasis on Arizona is understandable, of course, and New Mexico and southwestern Colorado are also well represented. Utah's Hovenweep, too, is prominently featured. The puzzle is why ground zero Utah points like Edge of the Cedars and Anasazi state parks, and a few national parks with artifacts, receive no mention whatsoever.

But that is certainly a minor riddle considering the much more significant questions that are the focus of this fascinating book.

In the last pages, Cheek considers the various factors thought to have contributed to what archaeologists call the "abandonment." Speculation still swirls, he says, but "almost certainly there was an intricate web of reasons. Too many people, too little (or too much) rain, erosion, aggression, disease, soil too poor for farming, systems of government too sluggish in responding to crisis. None of this is unusual in human history, which is why the word `mystery' should be divorced from the abandonment."