  The work done by Isaac Newton more than three hundred years ago, continues
being a path to increase our knowledge of Nature. To better understand all the
ideas behind it, one of the finest ways is to generalize them to wider
situations. In this report we make a review of one of these enlargements, the
one that bears the mechanical systems from the elementary homogeneous three
dimensional Euclidean space to the more abstract geometry of a Riemannian
manifold.
