Theodicy

Theodicy is a branch of theology that seeks to explain why a God that is seen as all-loving, all-seeing, and all-powerful allows evil to exist. The word comes from the Greek words for God and Judgment and so means the judgment of God. It was first made up by the German philosopher Gottfried Leibniz in 1710 in his work "Théodicée". The subject has been the focus of argument and thought for hundreds of years before that and since.
Theodicy tries to explain why God, who has complete free will, has the power to change anything he wants to, can see all the evil in the world and is all-loving and compassionate, yet does nothing to alleviate the suffering in the world, especially the suffering of innocents.
The weakness of the arguments for Theodicy are often used by atheists to emphasise the problems that go with the belief in God.
Some arguments.
There are many arguments to try and explain evil; here is an incomplete list: