May 31 - June 12, 1864 In the overland campaign of 1864, Lieutenant General Ulysses S. Grant with the Army of the Potomac battled General Robert E. Lee and the Army of Northern Virginia for six weeks across central Virginia. At the Wilderness, Spotsylvania, North Anna and Totopotomoy Creek, Lee repeatedly stalled, but failed to stop, Grant's southward progress toward Richmond. The next logical military objective for Grant was the crossroads styled by locals Old Cold Harbor.