The standard grips this chord is usually shown with.
Amaj9 is A, C#, E, G# and B, a major ninth. The shape this page opens on is written x02424, lowest string first.

Also written AM9, AΔ9, Ama9 or A major 9. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 14 common shapes for Amaj9 on the guitar, and 39 derived voicings in 5 families.
In which keys. Every note of Amaj9 belongs to C# minor (the ♭VI), E major (the IV), F# minor (the ♭III) and A major (the I).
The common shapes, written lowest string first: x02424, x22224, xx2424, 522224, 546450, 546454, x06657, 576657, xx6657, xx7697, 977997, x-12-9-9-9-9, x-12-11-13-12-x, 12-12-11-13-12-x.
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. Amaj9 has 5464xx, x-12-11-13-12-x, xx7697.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Amaj9 has 5464xx, x-12-11-13-12-x, x2622x, xx6425, xx7697, 9-12-9-13-x-x, x-x-9-13-10-9, x4749x.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Amaj9 has x2x224, 5x642x, 7x769x, x-12-x-13-12-9, 9-x-9-13-10-x, x4x495, x-11-x-6-10-7.
Rootless. The root left to the bass player. Frees a finger for a tension. Amaj9 has x2212x, xx2424, x4645x, xx6657, xx9999, x-x-11-13-12-12, x-14-14-13-14-x, x2x120.
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. Amaj9 has x02424, 546400, 006657, 00660x, xx6600.
Tensions. A shell of Amaj9, root, third and seventh, leaves a string free, and the tones that belong over it are 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.