The American Civil War lasted from April 12, 1861 (when Confederates attacked the U.S. Fort Sumter off the coast of South Carolina) to April 9, 1865 (Robert E. Lee’s surrender to Ulysses S. Grant at Appomattox Court House, Virginia).
In between, as many as 8,000 hostile engagements took place between Union and Confederate forces. Included in these engagements were hundreds of major battles.
The U. S. Library of Congress features an American Civil War Time Line (link).
The National Park Service (link) maintains a listing and provides summaries of many of the major battles of the American Civil War.
The Civil War Preservation Trust maintains a list of battlefields (link).