Compare and contrast the eastern and western theaters of the war up through 1862. How did the military campaigns differ? What were the major battles and turning points of each?

Although the eastern theater generally receives more attention as it was closer to the coastal urban centers of commerce and government, as well as the scene of many large and bloody battles, the western theater may have been more important in the ultimate victory of the Union over the Confederacy. The battle of Bull Run established the pattern in the eastern theater of very costly Southern victories that never translated into a decisive military advantage.
In contrast to the eastern stalemate, the North was able to triumph consistently in the western theater of the Mississippi River Valley by first breaking through the Confederate line in Tennessee and occupying the western part of the state. The now strengthened U.S. Navy under Secretary Gideon Welles sailed into the mouth of the Mississippi and captured New Orleans, Louisiana. After the port city of Memphis was secured, Union troops advanced deep into the heart of the South overcoming all resistance until the battle of Shiloh where both sides took high losses. In addition to the river, General Grant was able to leverage the railroads to move troops and supplies to their advantage and the South was never able to regain the initiative.
In the eastern campaign the Union's drive to capture the Confederate capital of Richmond, VA was as bloody as it was unsuccessful and the North's troops were driven back. General Lee triumphed again at the Second Battle of Bull Run and advanced into Maryland. Lee had split his army and was greatly outnumbered but the ever hesitant General McClelland failed to press his advantage and take this opportunity to crush Lee's army. The ensuing battle of Antietam was a costly draw that allowed Lee to successfully retreat back across the Potomac with his army intact when McClelland might have crushed Lee army then and there. Lincoln fired him. Antietam did, however, permanently delay Great Britain's recognition of the Confederacy and hoped-for aid from Europe. By late 1862 the naval blockade of Southern cotton exports and the Confederacy's imports of necessary war supplies had begun to tighten.