I.Minkowski's Representation of Special Relativity -- Examples of Its Impact on the Twentieth Century Physics.- The Minkowskian Background of Whitehead's Theory of Gravitation.- The Experimental Verdict on Spacetime from Gravity Probe B.- Rigidity and the Ruler Hypothesis.-Minkowski Space and Quantum Mechanics.- Relativity and Quantum Field Theory.- Ether, the Theory of Relativity and Quantum Physics.- II: Implications of Minkowski's Ideas for the Philosophy of Space and Time.- Minkowski's Proper Time and the Status of the Clock Hypothesis.-Why Spacetime is not a Hidden Cause: A Realist Story.- Structural Explanations in Minkowski Spacetime: Which Account of Models?.-Relativity of Simultaneity and Eternalism: In Defense of the Block Universe.- Minkowski Spacetime and Thermodynamics.-No Presentism in Quantum Gravity.-III. The Impact of Minkowski's Ideas Beyond the Philosophy of Space and Time.- Spacetime, Phenomenology, and the Picture Theory of Language.- The Fate of Mathematical Place: Objectivity and the Theory of Lived-Space from Husserl to Casey.