So far we have introduced classical Newton mechanics which, however, has different transformation properties than Maxwell’s equations for electrodynamics. This incompatibility has been solved in Einstein’s special theory of relativity: we have to replace the Galilei transformation between inertial systems by the Lorentz transformation that keeps the velocity of light c invariant in all inertial systems. We will derive the Lorentz transformation explicitly (in a simple case) and discuss its implications: Lorentz contraction, time dilation, simultaneity in moving systems as well as causality and the limiting velocity of signals. Some mathematical aspects of the Lorentz group of transformations will be discussed and Lorentz scalars, four-vectors and Lorentz tensors are identified as well as corresponding physical quantities like four-current densities. We close the discussion of relativistic dynamics by introducing the energy-momentum four-vector, which is conserved in all four components for closed systems and discuss scattering problems. As an example the important problem of Compton scattering of a photon on a resting charge q is computed explicitlyRelativistic mechanics. The derivation of the Lorentz transformation of the force will finalize this chapter.