The purpose of this article is to establish a sub algebra of an almost distributive lattice ℜ by defining the Core of ℜ notated by ℑπ for any π ∈ ℜ. The features of ℑπ are investigated. Some properties of R is characterised according to the structure of J_π. Moreover, the sets ℑ_ℜ,  ℑ_ℜ are introduced and ℑ_ℜ is proved to be a distributive lattice with 0. The relation between the set ℑ_ℜ and Birkhoff centre of ℜ is demonstrated.