The standard grips this chord is usually shown with.
Abmaj7 is Ab, C, Eb and G, a major seventh. The shape this page opens on is written xxx113, lowest string first.
Note by note. Ab is the root, C is the major third, Eb is the fifth and G is the major seventh.

Also written AbM7, AbΔ7, AbΔ, Abma7 or Ab major 7. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 7 common shapes for Abmaj7 on the guitar, and 29 derived voicings in 4 families.
One note away. Change a single note of Abmaj7 and you have Ab (with one note taken away), Abmaj7b5 (with one note moved), Abmaj7#5 (with one note moved), Abmaj9 (with one note added), AbmMaj7 (with one note moved) or Abadd9 (with one note moved).
In which keys. Every note of Abmaj7 belongs to C minor (the ♭VI), Eb major (the IV), F minor (the ♭III) and Ab major (the I).
The common shapes, written lowest string first: xxx113, xx1113, 465544, xx6888, x-11-10-8-8-8, x-11-10-12-9-x, x-11-13-12-13-11.
Under the hand. None of the shapes for Abmaj7 uses an open string, so every one of them is movable; the lowest sits at the 1st fret. 4 of the 7 need a barre. Together they cover the neck from the 1st fret to the 13th.
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. Abmaj7 has 435xxx, x-11-10-12-x-x, 4x55xx, x-11-x-12-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Abmaj7 has xx1113, 3311xx, xx5544, 4655xx, xx6888, x-10-10-8-9-x, 11-11-10-12-x-x, x-11-13-12-13-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. Abmaj7 has x3x143, 3x111x, x6x584, 4x554x, 8x688x, x-10-x-8-9-8, 11-x-10-12-9-x, x-11-x-12-13-11.
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. Abmaj7 has 4300xx, 3300xx.
Tensions. A shell of Abmaj7, root, third and seventh, leaves a string free, and the tones that belong over it are the 9 (Bb), the #11 (D) and the 13 (F).
What kind of chord this is. Abmaj7 is a major chord — root, major third, fifth. major chords on every root, and what they are for.
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.