Final answer:
General U.S. Grant's key military victories were at the Battle of Shiloh and the capture of Vicksburg. These victories allowed the Union to control river communications and force Confederate retreats from key areas, dividing the Confederacy.
Step-by-step explanation:
General U.S. Grant's military victories that allowed him to gain control of river communications and force Confederate troops out of Kentucky and Tennessee were pivotal during the Civil War. One significant engagement was the Battle of Shiloh, which took place in April 1862 near a church in Pittsburgh Landing, Tennessee. Despite being surprised by the Confederate attack, Union forces under Grant's command managed to hold their ground and eventually received reinforcements to drive back the Confederates.
The next major victory for Grant was the capture of Vicksburg, Mississippi, in July 1863, which followed a series of engagements wherein Grant used his superior numbers to push Confederate forces back, culminating in the siege and surrender of Vicksburg. This victory was essential as it granted the Union complete control over the Mississippi River, effectively bisecting the Confederacy and crippling its ability to maintain its eastern and western fronts.