Inductance

Inductance is a physical property that relates current through some conductor with magnetic flux through some other conductor. A high inductance means that for a small current we can get a large flux, and a low inductance means the opposite.

Self inductance

Self inductance $L$ relates the current through a coil with the magnetic flux through that same coil. Most often this comes up in the case of an inductor, a circuit element with a specific inductance.

To find the self inductance of a coil we can calculate the flux in terms of current and solve the equation above.

Alternatively, we can also calculate inductance using energy. The energy stored in an inductor is $U = \frac{1}{2} LI^2 = \iiint_V \frac{B^2}{2\mu_0}dV$. If we find the magnetic field in terms of current, and from that find the energy stored in the field as a whole, we can solve for inductance.