  The basic and fundamental aspects of General Relativity are in general
analysed in mathematical level of coordinate basis or holonomic frame by
several authors in the literature. However, for many purposes it is more
convenient to use a general basis, often called in four dimensions, a tetrad or
vierbein, very useful in a local frame with orthonormal basis or
pseudo-orthonormal basis. This text presents an introduction to non-coordinate
basis and the two Cartan's structure equations that are mathematical implements
in Riemannian geometry that facilitate the calculation of curvature tensors.
The purpose of this text is to approach the language and the notation of tetrad
field or vierbein with conceptual and calculational details.
