The tetrad formalism is an approach to general relativity that generalizes the choice of basis for the tangent bundle from a coordinate basis to the less restrictive choice of a local basis, i.e. a locally defined set of four linearly independent vector fields called a tetrad or vierbein. It is a special case of the more general idea of a vielbein formalism, which is set in (pseudo-) Riemannian geometry. This article as currently written makes frequent mention of general relativity; however, almost everything it says is equally applicable to (pseudo-) Riemannian manifolds in general, and even to spin manifolds. Most statements hold simply by substituting arbitrary n for n = 4 . In German, " vier " translates to "four", and " viel " to "many".