In this expository paper we present an introduction to the Curry Systems.
Over the past decades many non-classical logics have appeared and they have inspired
some algebraic structures underlying such systems. In this paper, we discuss some
applications of the concept of Curry algebra for algebraization of some paraconsistent,
paracomplete, and non-alethic logics. Such concept is also correlated with some fundamental
themes in logic, such as computability, constructibility, topology, and many
other basic branches.