The biographer of Marx, Lenin, Hitler, Stalin. . . can't miss with Trotsky, whose life is arresting in bare chronology. To Payne he is the Aichemedean ""who found the right lever and the right place to insert it,"" and proceeded to move the world; and Payne pursues him through a breathless sequence: from his beginnings as an audacious young rebel in and around Odessa, opposed to the ""dryness and hardness"" of Marxists but intent on first finding, then organizing the workers; to the brilliant oratorical feats of 1905 and 1917; to Red Army command during the Civil War riding victoriously through Russia on his ""locomotive of history""; to the pathetic long finale--Trotsky exiled and hounded by Stalin, but also rejected by every other government: ""Never had there been such unanimity among monarchy, the capitalists, and the Communists."" If the book cannot help but move fast, it does not reach deep. For lack of historical background and analysis, the dilemmas of the period within which Trotsky's theories and actions alone make sense, fail to project. Never, for instance, is War Communism even named, although it is the system which, from 1918 to 1921, ruled the young Soviet republic, Trotsky's dynamic stage. Consequently the giants of the Revolution--Lenin, Trotsky, Stalin--loom larger than they should, seeming to choose freely between good and evil. Payne's portrait of Trotsky, the ""old Bolshevik trapped within the murderous machine he helped to create,"" doubles as a morality lesson, more likely--whatever its faults--to engage the casual reader than Deutscher's celebrated three-volume classic, which remains unsurpassed.