Maxwell's equations… are they still in use? This is old school! It brings me back to my university courses ... (I may need a little refresher!) Come on, Maxwell's equations are the basic laws of physics constituting the basic postulates of electromagnetism. By digging a little, these equations result from different theorems (Gauss, Ampere, Faraday) governing electromagnetism. James Clerk Maxwell brought them together in the form of integral equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits They give a precise mathematical framework to the fundamental concept introduced by Faraday field in physics ...  Yes it is old and dates back to the 1830s. At the time however, they had little means to study these phenomena, neither extravagant HPC computations nor resources to study such a complicated matrix. Today, these formulas are widely adopted in some electromagnetic simulation software based on finite elements. They allow very accurate calculations of the magnetic of electric fields in static conditions, transient and harmonic. Far more interesting than a possible "Maxwell's equations for Dummies" book, you will definitely enjoy (like me) to rediscover the history of the people who developed the first unified theory of physics, and who progressively showed that electricity and magnetism are intimately connected, from the theory to the ultimate course of accomplishment in modern engineering.
"The Long Road to Maxwell’s Equations - How four enthusiasts helped bring the theory of electromagnetism to light"