Forty years ago this winter, I was an 8-year-old boy growing up on the North Side of Chicago. The Rev. Martin Luther King Jr. had moved into a slum in the impoverished West Side neighborhood of North Lawndale to dramatize the conditions of what were then known as "Northern Negroes." King was scheduled to visit the home of a local politician to raise money for his cash-strapped movement from white "lakefront liberals." But the politician, caught between his personal sympathies for King and his allegiance to Mayor Richard J. Daley, who was no fan of the civil-rights leader, felt uncomfortable hosting the party. So he called up my parents and, to my delight, the event was moved to our house at the last minute. The fund-raising was "disappointing," according to my father's diary, and King spent most of the evening on our telephone. But I got the great man's autograph and we heard him deliver an eloquent talk while standing in front of several dozen guests in our living room. At such events that year, King would sometimes scrawl a reminder to himself: "Ad lib 'We Shall Overcome'."

This all came to mind while reading "At Canaan's Edge: America in the King Years, 1965-68," the third and final volume of Taylor Branch's magisterial account of the most important social movement of the 20th century, which lasted only 13 years—from the Montgomery bus boycott of 1955 to King's death at age 39 in 1968. It made me think anew about how much has changed for African-Americans living in places like Chicago, and how little. In the aftermath of Hurricane Katrina, the unfinished agenda of the 1960s is under discussion again, if not in Washington then at least among the legions of local leaders still trying to better their communities.

Branch's book, to be published this month, shows us King not as a plaster saint but an intuitive, conflicted and harried human being—running late to everything, refereeing among squabbling lieutenants, straying from his wife to the end, even slipping out to catch what one of his traveling aides said was his favorite movie, "The Sound of Music."

But we also see that even after he became world-famous, King had reason to call his movement a civil-rights struggle. Branch conveys in powerful detail the dramatic, chaotic, inspiring and incendiary era, from the triumphant Selma-to-Montgomery march to the passage in 1965 of the landmark Voting Rights Act and little-noticed end to discrimination against the Third World in immigration (which reshaped the face of America); from the pathos of Lyndon Johnson—caught between his breathtaking commitment to fighting injustice and the worsening Vietnam War—to the backlash against liberalism represented by Ronald Reagan's election as governor of California, and finally to King's eerie "I might not get there with you" premonition at the Mason Temple in Memphis on the night before his assassination....