This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, space and time are not separate entities. They are combined into a four-dimensional spacetime continuum, which is most clearly demonstrated in the formulation of the theory of special relativity due to Hermann Minkowski. The chapter then defines vectors and tensors with respect to the Lorentz transformation, leading to a tensor formulation of Maxwell's equations, of the electromagnetic force acting on charges and currents, and of the energy-momentum of the electromagnetic field and its conservation law. It also introduces the energy-momentum tensor of matter and discusses the basic equations of the hydrodynamics of perfect fluids (the Euler equations).
On the Euler equations of incompressible perfect fluids