The 7th Chord (also known as dominanth 7th) adds another tone to the major triad chord. As the name implies the added tone is 7 steps from the root (following the scale). These chords are also called dominant chords and they are especially common in blues.
Dominant 7 chords
Dominant 7 chords with sharp or flat root
C#7 / Db7
D#7 / Eb7
F#7 / Gb7
G#7 / Ab7
A#7 / Bb7
Above you can see the chord names on top. The x letters and numbers indicate that the string shouldn't be played alternatively on which frets. These chords are not to be confused with the maj7 and m7 chords.
Barre chord shapes
The chord illustrated above is open chords (except the F7), but they could of course also be played as barre chords. The shapes for dominant 7th barre chords looks like this:
The diagram to the left depicts an E-shape barre chord for dominant 7th and the diagram to the right depicts an A-shape barre chord (the lowest string should not be played) in the same chord group. They are movable.
Movable shape with root on sixth string
This is an alternative way to play the dominant seventh chord. The shape is movable with the root note on the lowest string. One way to play it is by alternating thumb on the lowest string and when pluck the rest of the string with the fingers. Bass walks are of course possible and are useful in blues.
In jazz arrangements is often the tone on the b-string omitted.
Movable shape with root on fifth string
This is another alternative way to play the dominant seventh chord. Once again is the shape movable and this time is the root note on the A-string.
Movable shapes with root on fourth string
And last, here are two moveable alternatives with the root on the D-string (the fourth).
This is also a popular choice, but notice that this is a voicing. The root note is on the G-string (third string).