The literature on the war is so vast you could spend a lifetime reading really good books about it. Here are six excellent ones:
Battle Cry of Freedom (1988), by James McPherson: Widely regarded as the most authoritative one-volume history of the war.
The Fiery Trial (2010), by Eric Foner: A new Pulitzer-Prize-winning and authoritative account of President Abraham Lincoln's navigation through the politics of abolition; it won the Pulitzer Prize for History.
This Republic of Suffering: Death and the American Civil War (2008), by Drew Gilpin Faust: A moving examination of the ways in which the slaughter changed Americans' ideas on mortality and influenced the way they chose to remember the war.
Personal Memoirs of U.S. Grant (1885): it "surpasses any other military memoir of the Civl War and stands alone as the best presidential autobiography every published," says Joan Waugh, author of U.S. Grant: American Hero, American Myth (2009), itself a fine biography.
Robert E. Lee: A Biography (1934-35), by Douglas Southall Freeman: A portrait of the man in full four volumes on the leader of the Army of Northern Virginia.
Mary Chesnut’s Civil War (1981), edited by C. Vann Woodward: a collection of writings, in diary form, of the doyenne whose sharp eye and tart tongue left an indelible impression of civilian life in the South during the war years.