In this chapter tensors extend the concept of vectors and serve as a foundational framework for analyzing physical phenomena across classical and relativistic contexts. Central to relativistic physics are Lorentz-invariant quantities, such as spacetime intervals, energy–momentum relations and Maxwell’s equations, ensuring consistency across inertial frames. The four-dimensional dot product, utilizing the metric tensor \(g_{\mu \nu }\) , generalizes scalar products to 4D spacetime, underpinning key relations like \(E^{2} = p^{2} c^{2} + m^{2} c^{4}\) , which link energy, momentum and mass. Relativistic dynamics are governed by entities like four-velocity, four-acceleration, four-momentum and four-force, which integrate classical mechanics with relativistic corrections. Transformations of electric and magnetic fields between inertial frames illustrate the consistency of physical laws, while phenomena such as Lorentz contraction and time dilation underscore relativistic effects at high velocities. Lorentz invariance emerges as a unifying principle, maintaining the constancy of spacetime intervals, field relationships and invariant magnitudes of velocity and momentum four-vectors. The Lorentz gauge and continuity equation provide elegant representations of charge conservation and potential dynamics in spacetime. Relativistic kinetic energy relations integrate mass-energy equivalence, connecting classical energy concepts with relativistic formulations. This chapter bridges the gap between classical mechanics and special relativity, offering mathematical tools and insights for studying relativistic electrodynamic systems. It emphasizes the geometric and physical coherence of relativistic transformations, essential for understanding high-speed phenomena and electromagnetic field interactions.