Cartan's method of the Repere Mobile can be used to construct most of the
theorems of Fiber bundle theory and connections. The Cartan equations of
structure can be determined in a constructive manner. In particular, the
technique leads to an algebraic method of computing matrix of curvature 2forms
and the vectors of torsion 2forms.
More over the method demonstrates that there are two types of torsion 2forms 
a torsion 2form of translations (affine) and a torsion 2form of rotations.
The latter equation of structure is often ignored, but can be used to develop a
theory of disclinations.
