As I am very interested in Edward Zalta's research in Axiomatic Metaphysics, I wanted to read up on Formal Metaphysics. Would there be some introductory material that would help? Thank you in advance for your help!
I would direct your attention to property theory, which is a class of formal theories that try to formalize the notions of property and instantiation. For an overview of these I recommend Nino Cochiarella's entry on property theory in the Routledge Encyclopedia as well as Uwe Mönnich's and George Bealer's survey article on the same topic.
Relevant approaches include Peter Aczel's work on Frege structures, Raymond Turner's property formalisms as well as George Bealer's theory of hyper fine-grained intensional entities. There is also a somewhat dated but still highly readable collection of articles on the topic: 'Properties, Types and Meaning', Vol. I.