Basic four note chords
For the most part four note chords extensions of triads or altered triads, such as sus chords. In their most basic form a note is added on top, up a M3 or m3.
Four note chords can be inverted, but for the moment let’s not worry about that. The most common are 7, major 7, minor 7 , augmented 7, minor 7b5 (or half diminished) and fully diminished, e.g. : C7, Cmaj7, Cm7, C aug7, Cm7b5, Cdim7.