A Triad is a Chord consisting of 3 notes played simultaneously and is the smallest Chord in music.   Triads are primarily built up in stacked 3rds such as the C Major Chord, which has the notes C - E - G.   For the C Major Chord the 1st note of the Triad is the Root, which is C then a Major 3rd above that is E then a Minor 3rd above E is G.   As you can see below:

We can take all of the notes of a Major Scale and build 3rds above them to determine the types of Triads in a Chord Scale.  

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As you can see from the C Major Chord Scale there are 3 types of Triads revealed.   However, there are 2 more types of Triads so in Total there are actually 5 Triads:

The table below summarizes the 5 types of Triads and lists a Chord Formula, which shows how to alter the notes of a Major Scale to determine the notes for each Triad.   The 1 - 3 - 5 numbers are the Major Scale Notes to use.

  Major   C     1 - 3 - 5   C - E - G   Ma 3rd - Mi 3rd
  Minor   Cm     1 - b3 - 5   C - Eb - G   Mi 3rd - Ma 3rd
  Diminished   Cdim     1 - b3 - b5   C - Eb - Gb   Mi 3rd - Mi 3rd
  Augmented   Caug     1 - 3 - #5   C - E - G#   Ma 3rd - Ma 3rd
  Suspended Fourth   Csus4     1 - 4 - 5   C - F - G   P4 - Ma 2nd
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Inversions are simply a way to Rearrange the notes of a Triad or 4-Note chord in a different order when played.   All the Triads we have looked at so far have the Root of each chord as the lowest note, also referred to as the Bass note.

Root Position - The Root of the chord is the lowest note played or the Root is in the Bass.
Ist Inversion - The 3rd or 4th (sus4) of the chord is in the Bass.
2nd Inversion - The 5th note is in the Bass.
3rd Inversion - The 6th or 7th note of the chord is in the Bass. This only occurs with 4-Note chords, such as 6th & 7th chords.

Although 5, 6 & 7 note chords exist they are often voiced, which means not all of the notes are played as the chord tends to sound too muddy.   Examples:
  9th Chord - 5 notes   (CMa9, C9, Cm9, etc.,. )
11th chord - 6 notes
13th chord - 7 notes

When applying Inversions to Chord Symbols it is common to name the chord followed by a slash "/" to indicate what note is in the Bass meaning the lowest note of the chord to be played.   For example, Cm/G means to play a C Minor triad with G (the 5th) as the lowest note in the Bass.   The following chart shows Inversions for the C Major chord.
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It should be remembered that Inversions apply to 4 Part/Note Chords, as noted earlier for the 3rd inversion.