This chapter explores the foundational role of algebraization in the study of non-classical logics, particularly paraconsistent, paracomplete, and non-alethic systems. It highlights the limitations of classical algebraic methods, such as the quotient structure approach, when applied to logics where congruence relations are either incompatible or inadequate. The notion of Curry systems is introduced as a general and flexible algebraic framework capable of accommodating both classical and non-classical logical structures. Emphasis is placed on the development and utility of Curry algebras, pre-algebras, and pre-lattices, culminating in the formal definition of Boolean pre-algebras and ultra-pre-filters. The chapter also investigates the interplay between algebraic operations and logical principles, offering a comprehensive foundation for the algebraization of systems that admit contradictions without trivialization. This formal scaffolding enables deeper insights into logical systems and broadens their applicability in theoretical and computational contexts.