The **Galilean transformation** is used to transform between the coordinates of two coordinate systems in constant relative motion in Newtonian physics. The equations below, although apparently obvious, break down at speeds that approach the speed of light.

Unlike the Galilean transformation, the relativistic Lorentz transformations can be shown to apply at all velocities so far measured, and the Galilean transformation can be regarded as low-velocity approximations to the Lorenz transformation.

- The Galilean group: Here, we will only look at its Lie algebra. It's easy to extend the results to the Lie group. The Lie algebra of L is spanned by E, P
_{i}, C_{i}and L_{ij}(antisymmetric tensor) subject to