Short answers, pulled from the story.
The corps was a military innovation by Napoleon. It was formally introduced on the 1st of March 1800, when Napoleon ordered General Jean Victor Marie Moreau to divide his command into four corps. Napoleon fully developed the corps system in 1805.
According to the US Department of Defense, a corps typically consists of two to five divisions and anywhere from 40,000 to 80,000 personnel. The exact size varies greatly depending on the army and mission.
Congress legalised field corps in the United States Army by an act passed on the 17th of July 1862, during the American Civil War. Major General George B. McClellan had already planned to organise the Army of the Potomac into corps before the law passed.
The Canadian Corps maintained an identical composition from its creation to the Armistice, unlike British corps whose subordinate divisions were regularly reassigned based on operational requirements. It consisted of four Canadian divisions throughout the war.
Each corps d'armée combined cavalry, artillery, and infantry and was capable of holding ground against a numerically superior enemy. This allowed Napoleon to mass his forces against a weak section of enemy lines without leaving his flanks or supply lines exposed.
Corps is used for the diplomatic corps (foreign embassy staff collectively), the Peace Corps, the European Solidarity Corps, volunteer ambulance corps, the Salvation Army's local units, and bodies like the Examiner Corps for US patent examiners. The usage of ambulance corps traces directly to Major General McClellan's General Order No. 147 during the Civil War.