The Five Families of Chord and Scale Qualities

Augmented Chords (+)

Augmented Chords are in the Major family and are treated as altered Major chords.

Suspended Chords

The rules of all five families require a 3^rd to determine membership. A suspended chord replaces the 3^rd of a chord with a 2 or 4 (i.e. sus2 or sus4), and thus suspends membership in any one of them. The suspension creates tension which resolves back to a Major, Minor, or Dominant 7^th chord built on the same root.

Sixth Chords

In Rock, Jazz, and Blues a sixth chord (e.g. C6) is a shorthand notation for Major add 6. In classical music I believe it can also refer to the III chord in a Major key being used in inversion.

Minor 7 Flat 5 Chords

Minor 7 flat 5 chords are really half-diminished chords. I have heard lots of reasons why the was replaced with min75 (e.g. was possibly used for printer control codes in early computer typesetting) but I think music book publishers think that scary symbols will scare off potential buyers, so they flush an otherwise consistent naming system down the toilet.

Add Chords

An Add chord (Cadd9, or C7add9) has the quality of whatever the chord added to is.