Question: If you are playing in the Key C major, a chord progression can be as simple as C-F-G7-C or C-Am-F-G7-C.

What are the principles while using chords like Am7,Am6, Cdim7,Csus4,Cdom9,C13,Bflat,Aflat etc (many more which I have not written). When do you use these types of chord in the C major key? What are the guiding principles in the chord progression when these chords are also used in C major?

Answer: 
* Csus4 is used to suspend (delay) resolution to Cmajor (C6 or Cmaj7).
* Cdim7 is used as a passing chord from Cmajor to Dmin7, as in:

> 
> Cmaj > Ebdim7 > Dmin7
> 
> 
>
* Aflat has a dominant function in the key of C, so Ab is often used as a substitute for a dominant or subdominant
chord, so instead of

> 
> Cmaj > Fmaj > Cmaj
> 
> 
>

you may use 

> 
> Cmaj > Abmaj > Cmaj.
> 
> 
> 

Additionally, Ab7 is often used to resolve to or reinforce G7 which is the natural dominant chord in they key. 

* Am is simply the VI of the key, so it is used as a substitute for C6. Instead of major tonality (C6) you create a minor tonality (Am7).
* C dominant chords (C7, C9, C13) are used to modulate from the key of C to the key of F, as in the following:

> 
> Gmaj > C6 > Gmin7 > C9 > Fmaj
> 
>  Once you are in the key of F, you can modulate back to the key of C as follows:
> 
> 
> 

```
   > F6 > D7 > G7 > C

```
Those are often just notes add to chords to give a musical piece depth. Jazz players sometimes talk about coloring chords in with added sevenths and ninths.

Am7
This is just a chord with a seventh added. Regular solution of seventh should apply with these chords as well.

Am6 
Chords with sixths are usually passing chords where the sixth acts as middle man between two notes.

Cdim7
This is a chord commonly found when a seventh is added to the leading tone chord. The seventh is flattened and still has to resolve.