In this work different geometrical descriptions of gravity will be presented. From the linearised theory we will find symmetries required for a viability of gravitational theories; how to avoid ghost modes and undefined vacuum states. Then we will move to a full geometrical description of the gravity; at first standard General Relativity with the Levi- Civita connection will be mentioned, then a general affine connection will be used to show we still arrive at the General Relativity dynamics. Next, a geometrical setting based on the teleparallel space-time will be used in describing gravity, first using the torsion instead of the curvature, and then non-metricity. These will result in theories equivalent to the General Relativity. Extensions of gravity based on space-times equipped with the curvature, the torsion or the non-metricity will be presented. The Teleparallel Gravity will be analysed using a tetrad formalism. Last, the coupling of matter and geometry will be presented with a focus on fermion fields.