This is a novel about the Civil War. The generals and the battles, then, are ones you would expect to read about in a novel about this sad period in U.S. history.
The main character, Jethro, is always reading about the war in the newspapers and studying maps to see what is going on. In one chapter, he sees that southern generals Bragg and Smith have pushed the Union army back into Kentucky. Southern generals Robert E. Lee and Stonewall Jackson have won major battles over Union generals Pope and McClellan.
Shad writes a letter and describes the battle of Antietam. The Union is declared victorious, but the war is not over. After this, Lincoln fires McClellan and appoints Ambrose Burnside as general of the northern armies. There is mention of the battle of Fredericksburg and Stones River. Lincoln goes through many generals before he finally appoints Grant because "he fights" even though "he drinks." Shad also writes about the battle of Chancellorsville. The battle of Vicksburg is mentioned, and so is Gettysburg. In fact, Shad is critically injured at Gettysburg.
The novel ends with Sherman's famous "march to the sea" where this Union general totally plundered the South, joining forces with General Grant to finally defeat the South by cutting off supplies. Robert E. Lee finally surrenders to Grant.
I am sure I have left some of them out, but most of the major battles and generals are mentioned.