What was the process of restoring the south to the union after the civil war called

They call it the Reconstruction Era! But it was a massive fail as the administration had been exposed of corruption and once the armies left the south, subjugation of African Americans began and limitations were placed upon them.

I believe that the entire process was called "Reconstruction". After Abraham Lincoln was assassinated, the new President wanted to make it hard for the southern states to return to the Union after what they did.