Core Coil

What is the best way to measure/understand/design coil and inductance devices?
I was in a surplus shop with all kinds of inductors, coils, chokes, transformers, etc The variety of these devices is amazing.
How are these devices designed? How are they measured?
How do the turns/radius/core determine the inductance?
They are such basic devices, but I have never seen a standard multimeter capable of measuring it. Why?
Just curious how I would know how to measure and design them from scratch?
Thanks for any creative answers.
As for the multimeter question...I would assume it would have to do some kind of sweep through a large range of frequencies to measure it property? Thx
Inductor come in a large variety of forms, depending on their inductance value, current ratings, and applications. They all consist of coils of wire basically, and these coils can be wound around air cores, iron cores, ferrite cores. Some inductors have cores that can be moved in and out of the coil to vary the inductance. RLC meters measure inductance with an AC signal; some mulimeters measure the current rise with time with a constant applied voltage. There are also impedance bridges which match the inductance to reference components. The basic unit of inductance is the Henry. A current rise of 1 ampere per second with an applied constant voltage of 1 volt represents an inductance of 1 Henry. One Henry is a very large inductance, with most inductors valued in the microhenry or millihenry range.
To design inductors there are formulas involving coil diameter, number of turns, and permeability of the core. For more information see http://en.wikipedia.org/wiki/Inductor
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