Grandfather Paradox

If you travelled back in time and caused yourself to never be born then you would not be able to go back in time and cause the event because you were never born. This paradox is known as the grandfather paradox. 

A common example of the grandfather paradox is if you got in a time machine and visited your grandfather before he had your father. If you shot him then your father wouldn't be born and neither would you, but then there is no one to shoot him because his assassin was never born. 

That is the grandfather paradox.