The Monadology is a compact statement of Leibniz's mature metaphysics, written near the end of his life and set out as ninety numbered paragraphs that build on one another like steps in a proof. Latta's 1898 translation presents it with the running commentary that has made this edition a standard English entry point to Leibniz's thought.
Leibniz starts with the smallest question and works outward. Because anything compound is just an aggregate of simpler things, there must be genuinely simple substances, and these he names monads. A monad has no parts, so it has no shape, no size, and no internal pieces that could be rearranged. It cannot begin or end by natural means; it can only be created or annihilated all at once. Famously, the monads have no windows, meaning that no influence passes in or out of them.
If monads are sealed off, how can they differ and change? Leibniz answers with two inner activities: perception, by which a monad represents many things at once, and appetition, the internal striving that carries it from one perception to the next. Every present state of a substance grows out of its preceding state, so its present is already big with its future. Minds, or rational souls, are distinguished by self-awareness and by knowledge of necessary truths, which lifts them above the bare monads that drift in a kind of stupor.
Two principles govern the whole system. The principle of contradiction sorts the true from the false, and the principle of sufficient reason demands that nothing be so without a reason why it is so and not otherwise. Pressing the second principle, Leibniz argues that the chain of contingent things cannot explain itself and must rest on a necessary being, God, who is the final ground of all reality. God surveys an infinite number of possible worlds and, by goodness and wisdom together, brings into being the one richest in perfection.
From this follow the doctrines the book is known for. Because God chose the best, the actual world has the greatest variety joined to the greatest order, and each monad reflects that whole from its own place. The agreement between soul and body, and among all substances, is not a constant series of interventions but a pre-established harmony arranged at creation, so that everything unfolds in concert. The work closes by joining physics to ethics: under this perfect government the universe forms a moral order in which the good are not finally neglected.