US Southwest: struggling land; The Southwest, by David Lavender. New York: Harper & Row. $15.

Here is an illiminating narrative of the settling of the American Southwest from primitive times to the present. "The Southwest" places under magnifying glass the conflicts marking the development of what author David Lavender calls "one of the poorest, most strife-torn regions in the nation." The battles, he says, swirled over issues of race, empire, gold, land, water, economic privilege, and politics.

The author's account of the desperate struggle over water rights particularly , for irrigation and industrial purposes, provides an excellent basis for understanding the future of this parched and thirsty but increasingly crowded land. And his account of the merciless clashes over cultural and racial issues -- mainly involving Anglos, Hispanics, and Indians -- shows us what elements of the human mind will need to be tamed everywhere if men are really to live on this planet as brothers.

What impressed me most about the book was its close-in description of these clashes of alien cultures, much of it contained in a masterful chapter entitled "The Anvil of American Indian policy."

In the early 1700s, Lavender writes, Spanish missionary priests theorized that it would take 10 years to re-orient the culture of the Southwest Indian tribes. but more than 200 years of unbelievably cruel conflict followed, and the issue still is not fully resolved.

In his comments on the vicious warfare resulting from efforts to corral the nomadic Indian tribes onto ever-diminishing reservations -- with all the suffering, pillage, and outrage this involved on both sides -- Lavender includes an especially poignant quotation. Said Ten Bears, a Comanche who negotiated with the American "peace commission": "I was born upon the prairies, where the wind blew free and there was nothing to break the light of the sun. I was born where there were no enclosures and everything drew a free breath. I want to die there and not within walls."

Lavender also calls attention to the insidious role which racial stereotypes have played, and still play to some extent, in notes, for example, that in the days when statehood for New Mexico and Arizona was under consideration, one thing that held up the proceedings was "a belief held by many of the nation's policymakers that both regions were the haunt not of civilized peoples but of murderous Indians, fiery Mexican bandits, cattle thieves, professional gunmen, drunken miners, conniving businessmen, sly speculators, and corrupt politicians."

Examining how such stereotypes came to be accepted, he comments provocatively: "Altogether it is a story not without relevance to some of the darker aspects of the American character today."

One could extend his point further since prejudicial stereotypes are damaging whenever they exist. On the national and world scenes they need to be rooted out if good will is to prevail. What about the harsh attitudes prevailing between disparate cultures of the Mideast? What about the cultural and nationalistic stereotypes in eastern Canada, or in America's various ethnic enclaves?

The underpinnings of his book also deserve to be noted. Lavender's exploration of the history, peoples, geography, and problems of the American Southwest has spanned most of his adult life, and he has published some 20 books on various aspects of Western history.