What were the primary strategies employed by the North and South in the Civil War?

In the Civil War, the North tried to encircle the South and then cut it apart.  The South could have stood on the defensive, but it did not. Instead, it tried to take the fight to the North so that it could break the North’s will to fight and, perhaps, gain international recognition.

The North wanted to encircle the South to prevent it from getting the supplies it needed.  It tried to do this mainly through a naval blockade.  Then, it tried to invade the South and cut it apart.  It attacked down the Mississippi River, taking control of that river and cutting the western part of the CSA off from the east.  It attacked along the Tennessee River and then took Atlanta, cutting the Deep South off from the northern parts of the CSA.  All this time, it used its superior numbers and material wealth to pursue a strategy of attrition, wearing the CSA down and destroying its ability to fight.

The CSA could have simply defended its territory without trying to invade the North.  However, for a variety of reasons, it did not wish to do this.  Instead, it tried to attack the North.  The most famous instance of this was in its invasion of Pennsylvania that ended with the Battle of Gettysburg.  The South hoped to make it clear that the North could not defeat it.  It hoped to attract recognition from Europe that it was a sovereign country.  If it had achieved either of these, it may have won its independence.