This chapter provides a comprehensive treatment of Heyting algebras as pre-algebraic structures modeling intuitionistic logic, emphasizing their constructive and topological interpretations. In contrast to Boolean algebras, Heyting algebras reflect the constructive nature of truth, where the Principle of the Excluded Middle does not hold. The chapter develops foundational definitions and equivalences between Heyting algebras and propositional Heyting algebras, introducing the constructibility operator “o” to connect logical semantics with computability and topological structures. It explores generalized topological spaces, duality via closure-like operators, and ideality operators that bridge constructive and classical reasoning. Finally, the concept of intentional operators is introduced to model intensional logic, highlighting the significance of non-monotonic behavior in algebraic frameworks. The treatment reveals the rich interplay between logic, algebra, computation, and topology, and positions Heyting algebras as central to constructive mathematics and computer science.