Maxwell’s equations

Maxwell’s equations form the basis of Electrodynamics, along with the Lorentz force law. The differential and integral forms are translated using generalisations of the Fundamental theorem of calculus, namely Острогра́дский’s divergence theorem and Stokes’s theorem. Note that Gauß’s law for magnetic flux and Faraday’s law of induction are automatically satisfied by defining the fields in terms of Electric and magnetic potentials.

Differential form

These use the mathematical language of Divergence and Curl.

The divergence of an electric field at a given point (how much field lines move away from that point) is proportional to the charge density at that point.
The divergence of a magnetic field is at all points, i.e. they do not diverge, since there are no monopoles. Thus a magnetic field is solenoidal.
Curl (tendency for field lines to orbit) in an electric field results in a change in a magnetic field, and vice versa.
Electric current passing through a closed circuit results in the magnetic curl, and vice versa.¹

These use the mathematical language of the Double integral, Triple integral; and more specifically closed Circulation and Flux

The nett number of electric field lines escaping through the boundary of some solid is proportional to the amount of charge contained within that solid (contained charge can be calculated using an integral over Charge density).
The nett number of magnetic field lines escaping through the boundary of some solid is always , i.e. the number of magnetic field lines leaving a space is equal to the number entering that space, since there are no monopoles.
Electric current moving anticlockwise in a closed loop creates a change in magnetic flux inside the loop in the direction of negative orientation.
Nett current moving through a cross section solid conductor or a change in electric flux cutting through (working together additively) results in a magnetic field circulating around the conductor, and vice versa.