Newtonian mechanics is only Galilei invariant. Therefore, it was necessary to find a covariant formulation of relativistic mechanics. This led to a modification of the classical equations of motion. By contrast, electrodynamics, i.e., Maxwell’s equations, are already inherently Lorentz covariant. This, however, is not evident from the formulation of the equations in terms of the electric field \(\boldsymbol {E}\) , magnetic flux density \(\boldsymbol {B}\) , electrical currents \(\boldsymbol {j}\) , and charge densities \(\rho _{\mathrm {el}}\) . In particular, neither \(\boldsymbol {E}\) , \(\boldsymbol {B}\) nor \(\boldsymbol {j}\) are four-vectors, and \(\rho _{\mathrm {el}}\) is not a Lorentz scalar. In this chapter we will present Maxwell’s equations in a covariant form. This will allow us to study the transformation behavior of electric and magnetic fields, as well as of charges and currents.