We review, in concise manner, the standard Einstein-Hilbert metric formulation of GR, together with related to it desccriptions such as the first order Palatini formalism, as well as the Einstein-Schroedinger pure affine formulation. We also describe the linerisation of the Einstein-Hilbert action around an arbitrary Einstein background, with associated geometric notions such as the Lichnerowicz operator. Some less standard aspects are also reviewed, for example we show how to explicitly rewrite the Einstein-Hilbert action in terms of the metric.