Moveable chord forms
Besides barre chords, there are many other moveable chords you can form. Most moveable chords are done on four strings, in four usual groupings: 'outside' chords, done on strings 1-4; 'inside' chords, done on strings 2-5; bass register chords, done on strings 3-6; and inside chords with sixth string bass notes.
To get an idea of how this is done, let's take the open G chord 
and move it up two frets to A:
| Outside A | Inside A | Bass register A | Inside A with 6th string bass |
 |  |  |  |
Minor chords