Relativity theory has enabled physics to take a great step forward. Nevertheless, unlike many of his followers, Einstein was not satisfied with his theory. In fact, in a 1947 letter to his friend Maurice Solovine he stated: "You imagine that deep down inside I regard the work of my life with calm satisfaction, the things are really different. There is not a single concept of which I am convinced that it will stand firm." Einstein"s concerns are analysed in the book From Galileo to Lorentz... and beyond. As demonstrated in the book, conventional relativity fails to answer several fundamental questions. A new set of space-time transformations is derived that cover a wider range of facts than the Lorentz transformations, and allow us to answer questions that are unresolved by conventional relativity. The implications for fundamental physics are far reaching.