Going back in time isn't so easy because of the light speed limit. However, it's nevertheless possible under certain assumptions. Goedel has proven this in the 1940s.

One of the assumptions is that you have a strong rotating gravity field. If the field is strong enough and rotates fast enough, there are closed paths that take you not only through space, but also through time - even backwards.

Still, there is no paradoxon. You can not go back and kill your father. The reason is that when you go back with the above method, you also need to move in space - so you end up at a position so far from you father's location that you'd need a gun with a bullet faster than light to kill him. And this, according to relativity theory, is impossible.