This chapter completes the study of classical electrodynamics by introducing Maxwell’s equations, a unified set of four fundamental equations that describe all classical electromagnetic phenomena. It begins by addressing the inconsistency of Ampère’s law in time-dependent regimes, leading to Maxwell’s intuition of introducing the displacement current ( \(\textbf{j}_D =\epsilon _0 \partial \textbf{E}/\partial t \) ). This crucial addition completes Ampère’s law, making it consistent with the charge conservation law and paving the way for the prediction of electromagnetic waves. The chapter then derives the d’Alembert wave equation for both electric and magnetic fields in vacuum, demonstrating that these fields propagate as waves at the speed of light ( \(c=1/\sqrt{\epsilon _0 \mu _0}\) ). This prediction, experimentally confirmed by Hertz, established light as an electromagnetic phenomenon. The structure of electromagnetic plane waves in vacuum is analyzed in detail, highlighting their transversality ( \(\textbf{E}\) and \(\textbf{B}\) fields are perpendicular to the propagation direction) and their mutual perpendicularity, forming a direct trihedron with the propagation vector. Various forms of light polarization are discussed, including linear, circular, and elliptical polarization, and their historical context and applications are briefly reviewed. Finally, the chapter introduces the concept of electromagnetic energy conservation through Poynting’s theorem. This theorem identifies the Poynting vector, which describes the direction and rate of electromagnetic energy flow, and the electromagnetic energy density. The chapter demonstrates how energy is transported and quantifies the intensity of electromagnetic waves, providing a complete picture of energy dynamics in electromagnetic fields.