Chords are part of the very fabric of traditional music. Evolving from the middle ages (before which music was generally 'plain' or simple melody) as an interesting addition to the church choir's technique. Building one note on top of another in various combinations allowed enormous expression to music which was quickly seized on by secular musicians.
The principles of chords and harmonies (and scales and modes) goes back at least to the ancient Greeks and the work of Pythagoras. Many musicians though developed the sense of pitch and harmony by ear - what sounded good. This happened to accord with Pythagoras's findings; in other words there was a reason for what sounded good and what didn't.
Today, chords are a familiar and possibly essential component in popular music and many people learn simple 'chord progressions' on guitars for accompanying songs. The classic '3 chord trick' is known to millions and has earned some a fortune!
This section is a mixture of practical advice for those who want to play chords on GDAE instruments, and theory for those who want to understand more about how chords are formed.