  In classical mechanics, there are two objectivities: The ``isometric
objectivity'' which concerns the constitutive laws of materials once expressed
in a reference frame, and the ``covariant objectivity'' which concerns the
universal laws of physics required to be observer independent. Covariant
objectivity is the main topic in this manuscript. We therefore first introduce
motions and Eulerian variables and functions, then we deduce Lagrangian
variables and functions, then define the function ``deformation gradient'',
from which we deduce simple definitions of the Lie derivatives. Then we detail
the construction of the velocity addition formula and recall the proof of the
objective covariance of the Lie derivatives. And constituvive laws built from
Lie derivatives are introduced.
