by Paul I. Wellman. Doubleday & Company. 402 pp. $6.

Mr. Wellman undertakes here to compress into one volume four centuries of the colorful history of the American Southwest, and very well he does it, too. He begins with Coronado’s fabulous march, discusses the gaudy colonial era in New Mexico, traces the adventures of early French venturers and explorers, and considers the genesis, growing pains and final incarnation of the great empire of Texas, with side-glances at Indian wars and cattle-country extravaganzas.