Barré (or Barre / Bar) Chords are chords of the same shape which you can use up and down the fretboard. Each position sounds a different chord, but the shape remains the same so it's easy to master.
These chord shapes work with any GDAE tuned instrument - Mandolin, Mandolin Banjo, Banjolin, Tenor Banjo, Octave Mandola, Bouzouki.
There are two sets of really useful barré chords to present here. They both run along the notes of the bass-most (G) string or course or the next highest (D). They give all the chords from G to F#, including all those you don't normally play or are hard to find like Eb. The first form is simple major/minor chords and the second, some simple variations which can give you major, minor, 6th and sevenths. The diagrams below will take you through it.
This is the first form of the barré chord explained. The index or first finger is the pink bar which is laid across all the frets at a particular position. The second or third finger is used to press on the second string or course two frets higher than the barré position. The 'x' means 'don't sound this string'. Try and damp it by lifting off the bar slightly on the first string or course only. It isn't a disaster if you don't, but you will get the sixth chord instead. Note that if you move your second (or third) finger back one fret, you will form the minor chord. The chord is the same as the note on the fourth string or course where the barré is i.e. :
This works on the next string up as well. In this case, don't sound the lowest string. The chord is the same as the note on the third string or course where the barré is. In the diagram, it is E major or E minor
So, by using barré chords between open and the seventh fret, you can play each of the 12 major or minor chords. Of course you can go higher than the seventh fret and on some instruments with longer scales like the tenor banjo or mandola this will work fine but it gets a bit trickier on the mandolin, mandolin banjo and banjolin.
This only works when the chord is following the note on the 4th string or course. Unless you have a cittern suitably tuned or a mandola with a fifth course! By adding a note on the 1st string or course, the ordinary major chord is enhanced and you don't need to 'stop' the 1st string.