One of the most important problems in the theory of operators is that of extension of a symmetric operator to a self adjoint one, so that the spectral theorem can be applied. Von Neumann gave the necessary and sufficient conditions for a densely defined symmetric operator to have a self adjoint extension in the same Hilbert Space. In case of Hermitian Operatpr when the domain of the operator is not dense in the Hilbert Space, it is not possible to apply Von Neumann theory as such. Coddington overcomes this difficulty by applying the theory of linear relations defined on a Hilbert Space. Coddington`s approach to construct a proof of the extension theorem was used, on the same lines as Von Neumann`s proof.