I Corps was the designation of three different corps-sized units in the Union Army during the American Civil War. Separate formation called the I Corps served in the Army of the Ohio/Army of the Cumberland under Alexander M. McCook from September 29, 1862 to November 5, 1862, in the Army of the Mississippi under George W. Morgan from January 4, 1863 to January 12, 1863, and in the Army of the Potomac and Army of Virginia. The first two were units of very limited life; the third was one of the most distinguished and veteran corps in the entire Union Army, commanded by very distinguished officers. The term "First Corps" is also used to describe the First Veteran Corps from 1864 to 1866.

Alexander McDowell McCook was a career United States Army officer and a Union general in the American Civil War.