Leibniz, like many thinkers of his time, was a theist - in other words he believed in God. He thought that the universe was composed of substances, chosen and maintained by God. He declared in his Theodicy that God created the world to be the best of all possible worlds, since God, as a benevolent deity, would not have created anything different. This is a difficult assumption for the modern reader to digest, as we are surrounded by examples of evil every day in the news.
Leibniz proves the existence of God by a priori and a posteriori arguments. Leibniz declares that there are two kinds of truth: truths of reason, and truths of fact. Truths of reason are a priori, while truths of fact are a posteriori. Truths of reason are necessary, permanent truths, and proceeding from a known or assumed cause to a necessarily related effect (deductive). Truths of fact are contingent, empirical truths relating to or derived by reasoning from observed facts (inductive) (Davidson, 91). Both kinds of truth must have a sufficient reason. Truths of reason have their sufficient reason in being opposed to the contradictoriness and logical inconsistency of propositions which deny them (Davidson, 93). Truths of fact have their sufficient reason in being more perfect than propositions which deny them. The Priori on pre-established harmony in so far as such harmony demands an author, and this is God. The posteriori explains everything that exists must have sufficient reason for existing, and this reason is God. (Davidson, 96)
Leibniz used the Monads to expedite his theory of God’s instilled harmony. His best known contribution to metaphysics is his theory of monads, as exposited in Monadologie (Monads). Monads are to the metaphysical realm what atoms are to the physical/phenomenal. They can also be compared to the corpuscles of the Mechanical Philosophy of René Descartes and others (Davidson, 109). Monads are the ultimate elements of the universe. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a pre-established harmony (a historically important example of panpsychism) (Davidson, 111). Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal. The ontological essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a preprogramed set of "instructions" constituted to itself, so that a monad "knows" what to do at each moment. (These "instructions" may be seen as analogs of the scientific laws governing subatomic particles.) By virtue of these intrinsic instructions, each monad is like a little mirror of the universe. Monads need not be quantum; in example each human being constitutes a monad. God, too, is a monad, and the existence of God can be inferred from the harmony prevailing among all other monads; God wills the pre-established harmony. Leibniz also claims, however, that the ultimate reason of all things must be found in a necessary and universal substance, which is God. A primary substance is not material, according to Leibniz, because matter is infinitely divisible. Every monad is produced from a primary unity, which is God. Every monad is eternal, and contributes to the unity of all the other monads in the universe.
Leibniz says that there is only one necessary substance, and that this is God. A necessary substance is one whose existence is logically necessary (Brown, 573). The existence of a necessary substance cannot be denied without causing some form of self-contradiction. Thus, God’s existence is logically necessary (Brown, 573). God is absolutely real, infinite, and perfect. All perfection and all reality comes from God. God, as the supreme monad, is an absolute unity. Leibniz explains that the perfection of a monad is revealed by its activity. The imperfection of a monad is revealed by its passivity. A monad is perfect insofar as it is active, and is imperfect insofar as it is passive. Actions and reactions are reciprocal relations between monads, and are constantly changing. The actions of some monads are a sufficient reason for the reactions of other monads. The reactions of some monads are given sufficient reason by the actions of other monads. All of the actions and reactions of monads are governed by a principle of harmony, which is established by God (Brown 578). Leibniz argues that, insofar as the rational soul or spirit can know eternal truths and can act according to reason, it can reflect God. The spiritual world is a moral world, which can guide the natural world. The goodness of God ensures that there is harmony between the spiritual world and the natural world, and establishes harmony between moral laws and natural laws. A perfect harmony of moral and natural law is found in the spiritual world, which Leibniz calls the City of God (Brown, 584).Leibniz also says that there are an infinite number of possible universes in the mind of God, but that God has chosen a single universe whose sufficient reason is that it is the best possible universe (i.e. having the highest possible degree of perfection) (Brown, 585). Monads are purported to having gotten rid of the problematic Interaction between mind and matter arising in the system of Descartes, as well as the lack of individuation inherent to the system of Spinoza, (which represents individual creatures as merely accidental) (Brown, 590).
Leibniz argues that since God is supremely perfect, and that therefore God has chosen the best possible plan for the universe. God’s plan for the universe necessarily produces the greatest amount of happiness and goodness, because it reflects God’s absolute perfection. The Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by an all powerful and all knowing God, who would not choose to create an imperfect world if a better world could be known to him or possible to exist. (Rutherford, 32) In effect, apparent flaws that can be identified in this world must exist in every possible world, because otherwise God would have chosen to create the world that excluded those flaws. The principal of suffiencient reason in “its classic form is simply that nothing is without a reason (nihil est sine ratione) or there is no effect without a cause”(Rutherford, 34) . As Leibniz remarks, this principle “must be considered one of the greatest and most fruitful of all human knowledge, for upon it is built a great part of metaphysics, physics, and moral science.” (G VII 301/L 227)(Rutherford, 39). Leibniz suggests that the claim that nothing takes place without a sufficient reason means that nothing happens in such a way that it is impossible for someone with enough information to give a reason why it is so and not otherwise. In the Monadology and elsewhere, however, Leibniz frankly admits that “most of the time these reasons cannot be known to us.” (Rutherford, 45). While the idea that every event must have a cause and that there is a reason why everything is so and not otherwise again might not seem novel, it is the connection that Leibniz sees between this principle and his other metaphysical principle that is noteworthy. According to Leibniz, Principals of sufficient must actually follow from principles of inherit notion (free will), for if there were a truth that had no reason, then there would be a proposition whose subject did not contain the predicate, which is a violation of Leibniz's conception of truth. (Rutherford 46)
But Leibniz’s arguments are very easily disputed. One such notion is the problem of evil. two main species of the problem of evil which Leibniz addresses is the “underachiver problem”. It argues that the evil in our world indicates that God cannot be as knowledgeable, powerful, or good, as traditional monotheists have claimed. The second, "the holiness problem," argues that God's intimate causal entanglements with the world make God the cause of evil (Blumenfeld, 20). God is thereby implicated in the evil at the expense of his holiness. Because reason and faith must be entirely reconciled, any tenet of faith which could not be defended by reason must be rejected. Leibniz then approached one of the central criticisms of Christian theism: (Blumenfeld, 22) if God is all good, all wise and all powerful, how did evil come into the world? Since leibniz argued God is the author of everything that exists, and evil is one of the things that exists, God is thereby the author of evil. And if someone is an "author of evil," they are thereby implicated in the evil and thus cannot be morally pure or holy. Thus, God cannot be morally pure nor holy. The answer (according to Leibniz) is that, while God is indeed unlimited in wisdom and power, his human creations, as creations, are limited both in their wisdom and in their will (power to act). This predisposes humans to false beliefs, wrong decisions and ineffective actions in the exercise of their free will. (Blumenfeld, 27) God does not arbitrarily inflict pain and suffering on humans; rather he permits both moral evil (sin) and physical evil (pain and suffering) as the necessary consequences of metaphysical evil (imperfection), as a means by which humans can identify and correct their erroneous decisions, and as a contrast to true good. Further, although human actions flow from prior causes that ultimately arise in God, and therefore are known as a metaphysical certainty to God, an individual's free will is exercised within natural laws, where choices are merely contingently necessary, to be decided in the event by a "wonderful spontaneity" that provides individuals an escape from rigorous predestination. The Theodicy has been critiqued as illogical by the philosopher Bertrand Russell. Russell points out that moral and physical evil must result from metaphysical evil (imperfection). But imperfection is merely finitude or limitation; if existence is good, as Leibniz maintains, then the mere existence of evil requires that evil also be good. In addition, Christian theology defines sin as not necessary but contingent, the result of free will. Russell maintains that Leibniz failed logically to show that metaphysical necessity (divine will) and human free will are not incompatible or contradictory. The core of Leibniz's solution to the underachiever problem is quite straightforward. Leibniz argues that there is no underachieving involved in creating this world since this world is the best of all possible worlds. Many thinkers have supposed that commitment to the claim that this world is the best of all possible worlds follows straightforwardly from monotheism. Since God is all-powerful, all-knowing, and all-good, there is certainly nothing that can prevent God from creating the best world. And God's goodness further obliges God to create the best world. Thus, the actual world is the best world. Leibniz's reasoning to his conclusion does not, however, follow this straightforward path since, among other things, it is not clearly cogent as it stands. It is easily seen that God would not be obliged to create the best if there were no best world. There might be no such best world if the series of possible worlds formed a continuum of increasingly good worlds. If there were no such best world, we cannot fault God for failing to create the best since to do so is as impossible as, say, naming the highest number. There is no such number of course, and likewise no such world. Thus, while God may obliged to create a world which has at least some measure of goodness, he could not be obliged, on this view, to create the best. Thus, God simply chose arbitrarily to bring about one among the range of morally acceptable worlds. One might think that declaring this world to be the best possible world is hardly a response to the underachiever problem. In fact, one might think it just provides ammunition for a new underachiever argument along the following lines; If God were all-powerful, all-knowing, and all-good, then this world would be the best possible world. But surely this world is not the best possible world, thus God is not all-powerful, all-knowing, and all-good.

Bibiliography
Davidson, Jack, 1996, "Untying the Knot: Leibniz's on God's Knowledge of Future Free Contingents," History of Philosophy Quarterly, 13: 89-116.
Brown, Gregory, 1988, "Leibniz's Theodicy and the Confluence of Worldly Goods." Journal of the History of Philosophy 26:571-91.
Rutherford, Donald, 1995, Leibniz and the Rational Order of Nature. Cambridge: Cambridge University Press.
Blumenfeld, David, 1994, "Perfection and Happiness in the Best Possible World." In The Cambridge Companion to Leibniz, Nicholas Jolley (ed.), Cambridge: Cambridge University Press.