Background
The Confederates won the race to Spotsylvania, and on May 9, each army began to take up new positions north of the small town. As Union forces probed Confederate skirmish lines on May 9 to determine the placement of defending forces, Union VI Corps commander Maj. Gen. John Sedgwick was killed by a sharpshooter; he was succeeded by Maj. Gen. Horatio G. Wright. Lee deployed his men in a trench line stretching more than four miles (6.5 km), with artillery placed that would allow enfilade fire on any attacking force. There was only one major weakness in Lee's line—an exposed salient known as the "Mule Shoe" extending more than a mile (1.6 km) in front of the main trench line. Lee recognized this weakness during the fighting of May 10, when twelve Union regiments under the command of Col. Emory Upton followed up a concentrated, intense artillery attack by slamming into the toe of the Mule Shoe along a narrow front. They actually broke the Confederate line, and the Second Corps had a hard time driving them out. Upton's attack won him a promotion on the spot to brigadier general, and it became a staple of military textbooks on how to break an enemy trench line. Similar tactics were used by Germany in its successful March 1918 offensive during World War I.
Seeing the danger, Lee began to lay out a new defensive line across the heel of the Mule Shoe that night, but before he could get it finished, Grant sent his entire II Corps of 15,000 men, commanded by Maj. Gen. Winfield S. Hancock, to attack the position in the same manner Upton had. This time, the breach in the Confederate line was complete, thanks in large part to an order from Lee that had already pulled much of the Confederate artillery back to the new line. The II Corps took close to 4,000 prisoners and probably would have cut the Army of Northern Virginia in half if the IX Corps (Maj. Gen. Ambrose E. Burnside), supporting it with an assault on the Confederate right flank, had pushed its attacks home with force. Instead, Lee was able to shift thousands of his men to meet the threat. Because of ineffective leadership displayed by Lieut. Gen. Richard S. Ewell, Lee felt compelled to personally lead Second Corps soldiers in the counterattack. His men realized the danger this would pose and refused to advance until Lee removed himself to a safer position in the rear. The battle in the Mule Shoe lasted for an entire day and night, as the Confederates slowly won back all the ground they had lost, inflicting heavy losses on the II Corps and the reinforcing VI Corps in the process. The angle between the II and VI Corps became known as the "Bloody Angle of Spotsylvania," where perhaps some of the most savage fighting of the whole Civil War took place. Whereas bayonet battles usually are very short, at the Bloody Angle, Union and Confederate troops fought with bayonets for hours in the same trenches.
By 3 a.m. on May 13, just as the Confederates had completed expelling the II Corps from the Mule Shoe, the new line was ready, and Lee had his battered men retire behind it. More than 10,000 men fell in the Mule Shoe, which passed to the Union forces without a fight. On May 18, Grant sent two of his corps to attack the new line, but they were met with a bloody repulse. That convinced Grant, who had vowed to "fight it out on this line if it takes all summer," that Lee's men could not be dislodged from their Spotsylvania line.
Grant, checked by Lee for a second time, responded as he had two weeks earlier. He shifted the weight of his army to the right flank and again moved to the southeast along roads Lee was unable to block. By May 20–May 21, the two armies were on their way to take positions along the North Anna River, another dozen miles closer to Richmond.

Aftermath

Spotsylvania Court House Confederate order of battle
Spotsylvania Court House Union order of battle