Maxwell's equations
The whole of classical electromagnetism — every static field, every circuit, every ray of light — is compressed into four equations. Maxwell's equations are that compression: the complete set of laws relating the electric field E and the magnetic field B to the charges and currents that produce them, and to each other.
In differential form and in vacuum (SI units) they are Gauss's law div E = rho/epsilon_0 (electric field lines begin and end on charge), the no-monopole law div B = 0 (magnetic field lines never end), Faraday's law curl E = -dB/dt (a changing magnetic field drives a circulating electric field), and the Ampere-Maxwell law curl B = mu_0 J + mu_0 epsilon_0 dE/dt (currents and changing electric fields drive a circulating magnetic field). Each has an equivalent integral form: the flux of E through a closed surface is Q_enc/epsilon_0, the flux of B through any closed surface is zero, the EMF around a loop is minus the rate of change of magnetic flux through it, and the circulation of B around a loop is mu_0 times the enclosed conduction plus displacement current.
Their crowning consequence is light itself. In empty space the equations combine into a wave equation whose speed is 1/sqrt(mu_0 epsilon_0), which turned out to equal the measured speed of light c — so light is an electromagnetic wave, and optics is a branch of electromagnetism. Everything downstream in this volume — potentials, energy flux, the stress tensor, the covariant tensor form — is just these four equations re-dressed.
Take Maxwell's equations in empty space, with no charges and no currents: rho = 0 and J = 0. Combining Faraday's law and the Ampere-Maxwell law gives a wave equation for E travelling at 1/sqrt(mu_0 epsilon_0) = 2.998 x 10^8 m/s — the speed of light, derived from two constants measured in tabletop electricity and magnetism experiments.
Four equations — two divergences, two curls — tie E and B to charge and current, and predict light at speed 1/sqrt(mu_0 epsilon_0).
These four are the microscopic (in-vacuum) equations, written with total charge and current; inside matter one uses the macroscopic versions with D and H. Faraday's law and the no-monopole law carry no sources — they are the structural pair — while Gauss's law and the Ampere-Maxwell law are sourced by charge and current.