Major 7th chords
The major 7th chord (abbreviated maj7 in chord names) is a four note chord, but due to the characteristics of the guitar the chords can involve four to six notes (in some cases with duplicated notes). The major 7th is not to be confused with the dominant 7th.
The chord is built by a root, a major third, a fifth and a major seventh. There are many ways to play these chords. Below you can see open maj7 chords presented and by scrolling down further you could also see maj7 played as barre chords.
Open major 7th chords
Maj7 chords with sharp or flat root
Some major seventh chords with sharp or flat root in short natation:
F#ma7 / G#ma7: XX4321
The dots indicate there your fingers should be placed. X means that the string shouldn't be played at all and the numbers indicate frets (0 means that the string should be played open).
Some suggestions of chord progressions including maj7 chords.
A - Amaj7 - Dmaj7
Bm7 - E7 - Amaj7
D - Dmaj7 - Em7 - F#m - D
C - Cadd9 - Cmaj7 - Am
D - Dmaj7 - G - Gmaj7
To look closer at this certain chord type we can take Cmaj7 as an example. Cmaj7 consists of four notes: C, E, G and B. Played as an open chord on the guitar it includes the following notes (from 5th to 1st string): C, B, G, B and E. The B note is duplicated, but not because it's the most important note, but due to the circumstance of the instrument and how it's tuned.
Movable barre shapes for major 7th chords
These two shapes can be used for all maj7 chords and the root note is the bass notes on the 6th and 5th strings respectively. The reason for the names "Emaj7-shape" and "Amaj7-shape" is that the shapes are based on Emaj7 and Amaj7 shapes in open position (see above). So, if you place the barre finger on the first fret and uses the Emaj7-shape, that makes you play Fmaj7.