First-Order Logic is the system of Symbolic Logic concerned not only with representing the logical relations between sentences or propositions as wholes (like Propositional Logic), but also with their internal structure in terms of subject and predicate. First-Order Logic can be considered as a kind of language which is distinguished from higher-order languages in that it does not allow quantification over subsets of the domain of discourse or other objects of higher type. Nevertheless, First-Order Logic is strong enough to formalise all of Set Theory and thereby virtually all of Mathematics. In other words, First-Order Logic is an abstract language that in one particular case might be the language of Group Theory, and in another case might be the language of Set Theory.