In the vampire diaries why does Damon come back to mystic falls please tell me why in the book series and in the TV show thanks?

Answer 1

Damon came back to mystic falls (in the TV show) to rescue Katherine from starvation, which he would have been successful if she was actually under there. In the book, she is under the church, but she isn't trapped, and Damon comes back to torment his brother, because he felt Stefan was responsible for Katherine's "death."

A Different Perspective:

In the TV show, Damon came back to get Katherine because the comet that he needed to cast the spell to free her had come back around. He thought that she was locked in a tomb under a church desiccating not starving, but it turned out that she wasn't there.

In the books, Damon thought he came back because he felt like tormenting Stefan for what happened between them and Katherine. They had both fallen in love with her so she 'killed herself' to 'bring them together', but they just ended up killing each other. It turned out that she wasn't really dead and she used her Power to subconsciously make them decide to go to Mystic Falls.