In Epistemology, Leibniz was in the Rationalist tradition being influenced by Nicolas Malebranch and Antonie Arnauld (disciples of Rene Descartes).
In Philosophy of Mind, Leibniz held the doctrine of Pre-established Harmony: since mind and body are different substances, they cannot causally interact with one another. Physical causality and mental causality run on parallel tracks (which explains temporal correlation) which were each created and set in motion by God.
In Ontology, Leibniz proposed monads as the fundamental particles which constitute the universe. Unlike atoms, monads are eternal, simple, indestructible, mental substances that act according to the predetermined will of God. Though they appear to interact with one another, each is following its own peculiar destiny which creates the appearance of causal interaction.
In Philosophy of Religion, Leibniz held that God’s omnipotence, omniscience, and omnibenevolence insured that the universe is the “best of all possible” universes. This includes the Principle of Plenitude which requires the actualization of all genuine possibilities to form the best of all possible realities.
In Logic, Leibniz proposed the Law of Identity and the Law of the Identity of Indiscernibles. The Law of Identity holds that for any true proposition, its contradiction must necessarily be false. The Law of the Identity of Indiscernibles holds that no two distinct things can have an identical set of properties (or negatively stated, any two things with an identical set of properties are not really two different things).
Read more about Gottfried Leibniz.
Read a more detailed article about Leibniz from the Internet Encyclopedia of Philosophy.