Chord Roots and Chord Inversion

Chord Roots:

The Root of any chord will be the note which corresponds to the letter name of the chord. For example, the root of a C-Major chord is C. If a chord is in root position, the root will always be the lowest note in that chord. The following chord is a C-Major chord in root position, containing the notes C, E, and G:
C-Major chord in root position


Chord Inversion:

If the root of a chord is not in the bass (the lowest note in a chord voicing) then that chord is said to be an Inverted Chord. For example, starting form lowest to highest, if you have the notes E, G and C, you have an inverted C Major chord. It is inverted because the C, the root of the chord, is not in the bass. It does not matter what in order the notes are arranged, as long as the chord has the same notes as the root position chord. For example, in the following chord we have the notes E, G, and C:
Inverted C-Major chord
This is an inversion of the C-Major chord. It is still a C-Major chord, but just with the notes rearranged. Any chord with the notes C, E, and G is a C-Major chord, no matter what order the notes are arranged, because they all contain the same three notes. The following example shows a C-Major chord in root position and inversions:
C-Major chord in root position and inversions
If the root of the chord is in the bass then the chord is in root position. If the third of a chord is in the bass then the chord is in first inversion. If the fifth of the chord is in the bass then the chord is in second inversion.
The following example shows differently spaced chords in root position or inversion. It only matters what the lowest note is to make it in root position or an inversion. The chord voicing (arrangement or spacing of the notes) does not matter:
C-Major chord in root position and inversions with different voicings
This principle of inversion applies to all chords, and also to chords with sevenths or other extended chords. The more notes a chord contains, the more inversions are possible. For example, seventh chords can have also have a third inversion, and ninth chords can have also have a third and fourth inversion.
Other Examples of Inverted Chords:
Other inverted chords
Extended chords in inversion