Abstract:
Among the Fundamental theorem of Functional Analysis, we study that the “Versatile Hahn –
Banach Theorem on the context of real linear vector space and on normed space (Banach
Spaces) in its two principal forms which are the continuous extension theorem ( Analytic
version) and the separation theorem (Geometric version). We began by discussing some
preliminaries that helps to formulate the statement of the theorems along with some definitions
that are required to understand these statements and we also prove some of these theorems and
discuss some of its important properties, consequences, and its applications. The whole thesis out
lines that these theorems are applied in many disciplines, we make some comments that give
condition for the theorems as a power full principle of functional analysis
