Grr!.... I've misplaced my #$%$ theory books.

I need information about augmented 6th chords.
Can anyone help refresh my mind?
I remember...
There are Italian, French, and German augmented 6th chords.
What is the function? Pre-dominant? What type of chords do they come from, and move to?
What's the voice leading for the individual chord tones?
How did these chords come to be? The historical evolution side.
What poing of music history were these used? What styles?
To answer my own questions a little.... and do you find this all correct?....
It +6 is #4, b6, 1
Fr +6 is #4, b6, 1, 2 It's the symmetical one
Gr +6 is #4, b6, 1, #2 It's the one that can be respelled with #2 as b3 to create a dominant 7th and move to a different key right?
I suppose the #4 and b6 are resolving to the dominant and the 1 is moving down to the leading tone on the dom 7.
There called augemented 6ths because that's the interval from the b6 to the #4. I don't why I spelled them like that up there then. The only position for them is in b6 #4, right? Not much room for inversion because then it's not a +6 interval, right?
I forget if there's anything with doubling certain notes or taking care for certain situations that would produce parallel's...
These chords made me wonder if you could take any group of notes and call it a chord, as long as there's some justification for how the notes move.