Earlier this year, when President Obama announced from the East Room of the White House that he and his wife, Michelle, and their two daughters would travel to Selma, Ala., to commemorate the 50th anniversary of the civil rights marches there, he said they did so “not just as a president or a first lady or as ­African-Americans, but as Americans.”

It was only the latest time Obama assured the nation that he represents all Americans, not just those who identify with him as the first black president. Three decades before, in an eerie bit of foreshadowing, a Princeton University senior named Michelle Robinson read a book for her thesis about the challenges faced by black politicians — challenges that would later resurface again and again throughout the political career of her future husband. The authors, she wrote, “discuss problems which face these black officials who must persuade the white community that they are above issues of race and that they are representing all people and not just black people.”

In “Michelle Obama: A Life,” Peter Slevin quotes friends and colleagues who describe Mrs. Obama as “confident” and “poised” and “extremely articulate.” But she also comes across in this thoughtful biography as constantly searching and frequently torn between different worlds — not just black and white but also ­working-class and elite. In the early chapters of this portrait, race influences everything in Mrs. Obama’s life — from her family’s roots in slavery and segregation; to the Black Belt of Chicago with a street named after Emmett Till; to the South Shore Country Club that had not allowed ­African-Americans to join, but where, in 1992, the Obamas held their wedding reception.