If God is so great, how does evil exist?

        If god is all-good and all-powerful, why would he allow evil to exist?
        There are two basic types of evil in the world, moral evils and natural evils.  Moral evils are caused by the free will of people, so God can't be blamed for them.  Natural evils, such as natural disasters, diseases, and death are harder to explain.  God should be able to prevent them.  The existence of these natural evils suggest that God could not exist.
        The only explanation for God to allow evil is that good would somehow come out of it.  Assuming God is all-good and all-powerful, he wouldn't directly allow evil for no reason.  Therefore there must be good brought about by the evil.
        "Good can exist without evil, whereas evil cannot exist without good."  Evil is the absence of good, and all things are good by nature.  All material things are susceptible to corruption however, and this is a necessary fact.  Evil has no direct cause; it is only caused accidentally.  For example, the better a fire is, the more it harms what is around it.  The fire itself is not evil; its goal is not to destroy but to perfect itself, and by doing so it accidentally causes harm.  Overall, evil cannot wholly destroy good.
        Another example is in predators and prey.  A lion could not live if it did not kill prey to eat.  It is not evil because it is simply doing what is necessary for it to live.  The evil in this case is indirect and accidental.  Evil is necessary to perfect the universe.
        As Augustine says, "Since God is the highest good, He would not allow any evil to exist in His works, unless His omnipotence and goodness were such as to bring good even out of evil."  This is partly was makes God so infinitely good.
        I wrote extensively about my views on the problem of evil in my work, Summa Theologica.