Galilei invariance

The most important aspects of the Galilei invariance are discussed as well as some physically important representations of the homogeneous and inhomogeneous Galilei groups. It is immediately possible to get Galilei covariant relations from the analogous Lorentz covariant ones. Some peculiarities are arising: The degeneration of the metric tensor prevents the usual transformation from co- to contravariant quantities, the physically important representations of the inhomogenous Galilei group are essentially projective, and the physically important finite dimensional representations of the homogeneous Galilei group are not completely reducible. From these peculiarities some obvious differences with regard to relativistic physics are emerging