Galileo and others considered only inertial reference frames (see the discussion of such frames in frame of reference) in uniform translation relative to each other. The measurement of time was assumed to be the same for all observers, but the measurements of distance made by an observer differ from those by another depending on the relative velocity between the observers’ frames of reference. The measurements made by one can be transformed to those by another one. Such a transformation is called the Galilean transformation.
Einstein saw, however, that if the vacuum speed of light was really the ultimate velocity in our physical world, a different kind of transformation was called for. If information about an important event cannot reach us faster than light (or any form of electromagnetic phenomena) can, the Galilean assumption of universal time has to be discarded. We can only do physics based on what we can know; physics based on mere, unsupported suppositions has to be ignored. The transformation of an observer’s measurements to another observer’s measurements, now changed, is called the Lorentz transformation. For details, see Theory of Relativity and Special Relativity.
General Relativity extended the Principle of Relativity to accelerated frames of reference in a gravity field.