The general theory of relativity, as a classical theory of gravitation, is based on a unique Levi-Civita connection, which is entirely given by the metric tensor of a given smooth manifold. The uniqueness of the Levi-Civita connection is based on the assumptions of vanishing torsion tensor and compatibility of the metric with the covariant derivative, or in other words vanishing non-metricity tensor. As a consequence of this formalism, gravitation is entirely given by the properties of the Riemann curvature tensor, or with the curvature of a given spacetime. In this text, we are exploring the consequences of relaxing the aforementioned assumptions and we conclude that there exists a dynamical equivalence between the general theory of relativity with theories based on a vanishing Riemann curvature tensor, and simultaneously nonvanishing torsion and non-metricity tensors, or with only non-metricity as a nonvanishing tensor, or with only torsion as a nonvanishing tensor. We also show that in this formalism there is a possibility of treating classical gravitation as a gauge theory based on the Lie group of translations. Furthermore, we look at given modified theories of gravitation in this formalism and we see that we end up with new dynamical models, which are in general different from dynamical models obtained from modified theories of the general theory of relativity. Those dynamical models are the subject of intense research, especially in the cosmological models.