Can a Relativistic Coordinate-Transformation be Covariant?

The Principle of Relativity is based on Galileo Galilei’s impeccable logic for which his inquisition-peers wanted to burn him at the stake. Here it is argued that subsequent physicists, already starting with Sir Isaac Newton, still formulated theories which are counter to Galileo’s logic. It is concluded that these theories, especially Einstein’s interpretation of relativity, have destroyed the cohesion that should have existed in our understanding of physics. Aspects of these theories and the experiments on which they are supposedly based, are tested against Galileo’s Principle of Relativity These analyses point to better interpretations of physics which do not need fudges like "dark matter", "dark energy", "time-dilation", "length-contraction" "four-dimensional space-time", "singularities" "point particles", and "renornalization".