About Am/G — uncommon voicings
Am/G is G, A, C and E — with G put in the bass.
It sounds like the minor triad it is, resting on a different floor. If G is already one of the chord’s notes this is an inversion, and if it is not it is a new colour under an unchanged chord; either way the reason to reach for it is a bass line that walks by step where root-position chords would leap.
Inversion or pedal — the harmony is unchanged; only the bass moves.
Also written Am over G or Am with G in the bass.
What these less common shapes are
How to use Am/G
In which keys. Every note of Am/G belongs to C major (the vi), D minor (the v), E minor (the iv), F major (the iii), G major (the ii) and A minor (the i).
What to play over Am/G
Every note of Am/G is in A minor pentatonic, A blues, A natural minor, A dorian and A phrygian.
Each of those is a page: the scale across the neck, and the chords it harmonises into — which is where Am/G sits in it. Every scale.
Chords near Am/G
Change one note of Am/G and you have (drop the flat seventh), (the flat seventh becomes the sixth), (the fifth becomes the flat fifth), (add the ninth), (the flat seventh becomes the major seventh) or (the flat seventh becomes the ninth).
Am/G is a slash chord — a triad over a named bass note. Slash chords on every root.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.