Leibniz is well-known for his striking metaphysical views concerning substances and their relations to one another. Three such theses that Leibniz is widely read as advancing are the focus of this dissertation. According to the first thesis, no created substance can causally interact with any other. Each is independent of every other's causal activity and effects. According to the second thesis, no created substance can depend for its existence on any other. The existence of each is metaphysically independent of every other: it is metaphysically possible for each to exist whether or not the others do as well. According to the third thesis, each substance has all of its intrinsic properties essentially, and could have no other intrinsic properties. No actual substance that God has actually created could exist and be intrinsically any different than it in fact is. Moreover, for every possible substance that God could have created but did not, it could have been created with one and only one intrinsic profile. That Leibniz accepts the first thesis, concerning substances' causal independence, has been nearly universally accepted by commentators. That Leibniz accepts the third thesis has been perhaps the most widely accepted interpretation of Leibniz's essentialism. That Leibniz accepts the second thesis, concerning substances' existential independence, has been a prominent view but is still controversial among commentators. My three main claims in this dissertation are, first, that Leibniz accepts the second thesis, but on grounds commentators have not yet noticed. Second, I argue that Leibniz is committed to the first thesis, but again for reasons that commentators have not seen. Third, I establish for the first time that these three theses are mutually entailing, a metaphysical package deal.