The standard grips this chord is usually shown with.
Am7 is A, C, E and G, a minor seventh. The shape this page opens on is written x02010, lowest string first.

Also written Amin7, A-7 or A minor 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 9 common shapes for Am7 on the guitar, and 38 derived voicings in 4 families.
In which keys. Every note of Am7 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).
The common shapes, written lowest string first: x02010, x02213, xx2213, 575555, xx7988, x-12-10-12-10-x, x-12-10-12-13-x, x-12-14-12-13-12, x-x-14-14-13-15.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. Am7 has 535xxx, x055xx, x-12-10-12-x-x, x0x01x, 5x55xx, x-12-x-12-13-x, 5-10-10-x-x-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Am7 has xx2213, x0201x, 3322xx, xx5555, 5755xx, xx7988, x-10-10-9-10-x, 12-12-10-12-x-x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Am7 has 3x221x, x0x010, x3x253, x7x585, 5x555x, 8x798x, x-10-x-9-10-8, 12-x-10-12-10-x.
Open string. An open string left ringing against a fretted grip. Because it costs no finger, it sounds a note the closed shape has none left for -- a tension on top, or a pedal root underneath. Either a familiar grip with open strings added, or a shape so sparse the open strings carry the chord. These belong to their key rather than to a shape, so D, A, G and E have many and Eb a handful. Am7 has 535000, 57550x, 5x5500, 33220x, 030253, 530000.
Tensions. A shell of Am7, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (B), the 11 (D) and the 13 (F#).
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.