  This is the lecture 2 of a mini-course of 4 lectures. Our purpose of this
mini-curse is to explain some ideas of E. Cartan and S. Lie when we study
differential geometry, particularly we will to explain the Cartan reduction
method. The Cartan reduction method is a technique in Differential Geometry for
determining whether two geometrical structure are the same up to a
diffeomorphism. This method use new tools of differential geometry as principal
bundles, $G$-structures and jets theory. We start with an example of a
$G$-structure: the 3-webs in $\mathbb{R}^{2}$. Here we use the Cartan method to
classify the differential equations but not to resolve. This is a
classification can be a weak classification in the sense of not involving all
the structural invariants.
