Walt Whitman: A Life, by Justin Kaplan. New York: Simon & Schuster. 429 pp.

With the slim, self-published edition of poems called ''Leaves of Grass,'' Walt Whitman emerged as America's first true poet. Among his freewheeling verses, as vigorous and pioneering as the country in which they were written, the ''courtly muses of Europe'' were nowhere to be heard.

Kaplan's biography gives us a full-blown portrait of Whitman and the social milieu that spawned and spurned him. It includes not only the details of his humble origin, self-education, apprenticeship as printer, work as journalist and teacher, his nursing of the wounded Civil War soldiers in the streets of Washington, but also interesting and amusing encounters with transcendentalist writers of his time. Ironically, though it met with English acclaim, Whitman's poetry was unrecognized in his own country during his lifetime.