The Lorentz Transformation is derived from only three simple postulates: (i) a weak kinematical form of the Special Relativity Principle that requires the equivalence of reciprocal space-time measurements by two different inertial observers; (ii) Uniqueness, that is the condition that the Lorentz Transformation should be a single valued function of its arguments; (iii) Spatial Isotropy. It is also shown that to derive the Lorentz Transformation for space-time points lying along a common axis, parallel to the relative velocity direction, of two inertial frames, postulates (i) and (ii) are sufficient. The kinematics of the Lorentz Transformation is then developed to demonstrate that, for consistency with Classical Electrodynamics, light must consist of massless (or almost massless) particles: photons.