If your definition of literature includes speeches and historical documents, Lincoln's Inagural Address together with the Gettysburg Address and the Emancipation Proclamation are certainly worth looking at. In these documents, Lincoln illustrates the irreconciliable arguments on slavery that have led to the conflict between the Union and the South. You can also look at Frederick Douglass's "An American Apocalypse" (1861) to see that the Union was not so easily persuaded that the abolishment of slavery should be one of the main points of their agenda and preferred to see the conflict as an effort to preserve the unity of the nation. Common people such as soldiers and civilians also wrote about the trauma of the civil war in journals and memoirs. The second links takes you to a comprehensive list of these contributions and primary sources.
As with other traumatic historical events, the American civil war has continued to attract the attention of writers well beyond its conclusion. In The Red Badge of Courage (1895), Stephen Crane used the memoirs of civil war soldiers, filtered through the war stories by Russian writer Tolstoy, to give a naturalist reconstruction of the civil war. To this naturalist foundation, Crane also added psychological depth and symbolic overtones. The war is potrayed in all its horror and the narratives emphasizes the alienation and loneliness of soldiers as well as the lack of free will and personal choice.
For a Southern perspective on the civil war, you could look at Thomas Dixon's novel The Clansman (1905), which served as the basis of D. W. Griffith's film Birth of a Nation. Making African Americans little more than caricatures, the novel exemplifies the appeal for white supremacy that characterized the post-reconstruction era. Margaret Mitchell's bestseller Gone with the Wind (1936) also offers a Southern perspective on the war together with a focus on the gender and class structure of Southern society and how this organization is affected by the conflict.