Robin D.G. Kelley’s new biography performs the essential and gratifying task of transforming a deliberately enigmatic eccentric—”I like to stand out, man. I’m not one of the crowd”—into a warm, familiar, flesh-and-blood presence. Kelley emphasizes that the chapeau-sporting genius who wrote “Nutty” was at bottom a devoted husband and father rooted in a social network dating back to his childhood on West 63rd Street in Manhattan, where he moved from North Carolina at age four in 1922. There Monk lived—except for two teen years in a gospel roadshow and a few sojourns with relatives in the Bronx—until he retreated to the Weehawken home of Baroness Nica de Koenigswater in 1976 and embarked upon his farewell silence.