Evil does not exist.
This at least was the assertion of St. Augustine, and I'm inclined to agree. In Platonic philosophy, God is identified with the Form of the Good, the realized Ideal. In Christian theology, God is viewed as perfectly good, a loving and benevolent deity. "God is love" is a foundational statement of our Christian faith.
The doctrine of the Trinity arose to rationally explain how the virtue of divine love can be found at the very heart or essence of God. For divine love is not self-love (we cannot say that God loves Himself), but the sacrificial love of oneself unto another (therefore we speak of the Three Persons of the Trinity, each of which participate in the perichoresis or divine dance, with the love of one for three and three for one). The doctrine of the Trinity is the defining characteristic of orthodox Christianity; therefore, we must assert that the doctrine of the benevolent and loving God is essential to Christian thought.
In Aristotelian philosophy, God is identified with the First Cause, the source and creative agency behind the universe. The relationship between Creator and Creation is sometimes treated in a deistic way by orthodox Christian monotheists. God exists above and beyond nature; He created it and then let it run freely, even if that means allowing sin to crop up. This treatment seems to diminish the sovereignty of God, not to mention His omnipresence (another essential doctrine of the Church).
Taking the doctrine of omnipresence seriously brings us to a theology closer to that of the Eastern Orthodox church, sometimes called 'panentheism' (though the term is quite problematic). Relying on such passages as Ephesians 4:6 (God "is over all and through all and in all") this doctrine asserts that God is the ultimate Substance ("sub-stance" = "that was stands below") underlying all reality, and that His Presence is required for anything and everything to exist.
God exists in the world, and the world cannot exist without Him.
Here is a separate tangential point, but an important one. If God is present within Creation, and God is love, then Creation must bear the fingerprints of its Creator. Therefore, Augustine argued against the Manichean heresy and asserted that nature and physical reality is first and foremost good.
This too is a core doctrine: nature is essentially good, and will be included in God's redemption.
But these arguments naturally leads to the problem of evil. How can evil be explained? For if God is both perfectly good and absolutely powerful (another essential Christian doctrine), evil should not exist. The existence of evil in the world demonstrates that either God is not perfectly good (for he is not willing to destroy evil) or God is not absolutely powerful (for he is unable to destroy evil). How shall we answer this syllogism?
Some choose to answer it by resorting to free will. God loves us and desires that we love Him, and therefore allows our free choice to obey or disobey, which leads to the existence of evil and sin and the corruption of nature. But while this answers the original dichotomy (God is perfectly good, but He expresses love in a different way than the philosophers would expect), it cannot answer a much more challenging question.
How can evil exist within the Presence of God? For if we take the doctrine of omnipresence seriously, and believe that God sustains all things in His being, then we cannot solve the problem of evil by resorting to free will. For even if God could passively allow evil to temporarily exist out of his love for us as creatures made in His image, no orthodox Christian could accept the doctrine that God sustains evil within His Presence. God is perfection; God is justice. Evil is fundamentally incompatible with God's being. How then shall we answer the problem of evil?
Augustine's answer is beautiful in its simplicity. He converted to Christianity after a brief fling with Manicheanism, which saw the spiritual Kingdom of Light and the material Kingdom of Darkness as the two cosmic force that would fight for all eternity. Augustine rebelled against this heresy, and argued that evil does not exist independently of the good, but is the negation of it.
Just as darkness exists only in the absence of light, so too evil can be said to 'exist' only where God does not. It is the absence of God. Evil is the vacuum in the fabric of space-time, the vortex in the middle of the sea. And if God is the ultimate Substance, the Presence that undergirds and sustains all that we know as reality, then evil does not exist. This does not mean that we do not feel its effects ; it only means that it has no independent substance and therefore will not endure. This is our source of hope and our hope for salvation; the good shall triumph and evil shall not exist.
This understanding will lead us to a doctrine of Hell, a doctrine that I (and, I imagine, most orthodox Christians) have wrestled with for quite some time. But with all mysteries, satisfaction can be found; with all challenges, growth follows. God is good, indeed.