  We discuss equivalent representations of gravity in the framework of
metric-affine geometries pointing out basic concepts from where these theories
stem out. In particular, we take into account tetrads and spin connection to
describe the so called {\it Geometric Trinity of Gravity}. Specifically, we
consider General Relativity, constructed upon the metric tensor and based on
the curvature $R$; Teleparallel Equivalent of General Relativity, formulated in
terms of torsion $T$ and relying on tetrads and spin connection; Symmetric
Teleparallel Equivalent of General Relativity, built up on non-metricity $Q$,
constructed from metric tensor and affine connection. General Relativity is
formulated as a geometric theory of gravity based on metric, whereas
teleparallel approaches configure as gauge theories, where gauge choices permit
not only to simplify calculations, but also to give deep insight into the basic
concepts of gravitational field. In particular, we point out how foundation
principles of General Relativity (i.e the Equivalence Principle and the General
Covariance) can be seen from the teleparallel point of view. These theories are
dynamically equivalent and this feature can be demonstrated under three
different standards: (1) the variational method; (2) the field equations; (3)
the solutions.
