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Three equivalent variational formulations of General Relativity Theory: 1)metric, 2) metric-affine (Palatini) and 3) purely affine, are discussed. Theclassical "Palatini method of variation" is thoroughly analysed. It impliesnon-metricity of the spacetime connection, as soon as the matter Lagrangiandensity is connection-sensitive. This conclusion is not new, but was neverseriously discussed. We show, that accepting this non-metricity, i.e. treatingboth geometric structures of spacetime: the metric tensor and the connection,as being a priori independent, but interacting with each other via fieldequations, considerably simplifies the conceptual structure of the presentGravity Theory and, maybe, provides a better starting point for itsgeneralisations from our Solar System scale to the Universe scale (darkmatter).

How the non-metricity of the connection arises naturally in the classical theory of gravity