This chapter presents the algebraization of first-order paraconsistent systems, introduced by Newton da Costa. These systems extend the propositional paraconsistent calculi Cn to the first-order level, maintaining the rejection of the Principle of Non-contradiction and allowing controlled contradiction. The formal syntactic structure of the systems is described, along with axioms, rules of inference, and the meta-logical behaviors they preserve, such as the deduction theorem and classical positive logic inclusion. The chapter proceeds to introduce the concept of Cn*-monadic algebras—an algebraic structure based on Curry algebras enriched with quantifiers—and investigates their semantic correspondence with monadic algebras. Representation theorems are proved, establishing connections with functional algebras valued over Boolean structures. These developments deepen the understanding of the algebraic foundations of non-classical quantificational logics and open new avenues for the study of paraconsistent quantification.