  The aim of this paper is to show certain properties of the Green's functions
related to the Hill's equation coupled with different two point boundary value
conditions. We will obtain the expression of the Green's function of Neumann,
Dirichlet, Mixed and anti-periodic problems as a combination of the Green's
function related to periodic ones.
  As a consequence we will prove suitable results in spectral theory and deduce
some comparison results for the solutions of the Hill's equation with different
boundary value conditions.
