  Weyl’s clarification of the role of coordinates, invariance or  symmetry principles, his important concept of gauge invariance, his  group-theoretic results concerning the uniqueness of the Pythagorean  form of the metric, his generalization of Levi-Civita’s concept of  parallelism, his development of the geometry of paths, his discovery  of the causal-inertial method which prepared the way to empirically  determine the spacetime metric in a non-circular, non-conventional  manner, his deep analysis of the concept of motion and the role of  Mach’s Principle, are but a few examples of his important  contributions to the philosophical and mathematical foundations of  modern spacetime theory. 