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You can find photos of these stitches in  Encyclopedia of Tunisian Crochet!
Tunisian Crochet: The Crossbar Foundations

IMPORTANT TIP: Due to the construction of the Cross Bar stitches, A LOOSE TENSION ON THE RETURN OF EACH ROW IS CRITICAL.  Otherwise, the Cross Bar is so tight, that you cannot get the hook through it to isolate the different threads/loop to create these new stitches.

The Cross Bar will look something like this:
[]<[]<[]<[]<[]<[]  The brackets are the vertical threads that you normally work with, and the arrow is the Cross Bar.

TOP THREAD
This is the most logical choice for using the Cross Bar as a foundation.   When looking at the piece of Tunisian Crochet, the Top Thread is the very top thread of the connecting Chain stitch that is made on the return pass.
STITCH INSTRUCTIONS:
Work the first row as you normally would for a Simple or Knit stitch.
2nd Row Forward: (SKIP THE FIRST CROSS BAR.) Insert the hk-front to back- through the center of the Cross Bar, making certain to pick up only the Top Thread of the stitch. Yo, pull through leaving loop on hk.  Repeat this across to other side, but work the last stitch as you normally would through the Vertical Threads on the end.  Return as you normally would for any other TC stitch.

THE BACK LOOP
When looking at the piece of Tunisian Crochet, the Back Loop is right behind the Top Thread of the Cross Bar.
STITCH INSTRUCTIONS:
Work the first row as you normally would for a Simple or Knit stitch.
2nd Row Forward: (SKIP THE FIRST CROSS BAR.)  Insert the hk,-top to bottom-through the Back Loop of the Cross Bar; making certain to catch only the Back Loop. Yo, pull through leaving loop on hk.  Repeat this across to other side, but work the last stitch as you normally would through the Vertical Threads on the end.  Return as you normally would for any other TC stitch.

BOTTOM THREAD VERSION #1
When looking at the piece of Tunisian Crochet, the Bottom Thread is the very bottom horizontal thread of the connecting Chain stitch that is made on the return pass.
STITCH INSTRUCTIONS:
Work the first row as you normally would for a Simple or Knit stitch.
2nd Row Forward: (SKIP THE FIRST CROSS BAR.) Insert the hk-from behind the bottom thread through the middle of the Cross Bar.  To do this, I insert the hook between the stitches just below the Cross Bar to work.  Allow the Crook of the hook to catch the Bottom Thread of the cross bar, and then pull the hook all the way through.  Make certain to catch only the Bottom Thread of the Cross Bar. Then, Yo, pull through leaving loop on hk.  Repeat this across to other side, but work the last stitch as you normally would through the Vertical Threads on the end.  Return as you normally would for any other TC stitch.


BOTTOM THREAD VERSION #2: Twist Up
When looking at the piece of Tunisian Crochet, the Bottom Thread is the very bottom thread of the connecting Chain stitch that is made on the return pass.
STITCH INSTRUCTIONS:
Work the first row as you normally would for a Simple or Knit stitch.
2nd Row Forward: (SKIP THE FIRST CROSS BAR.) Insert the hk-front to back- through the center of the Cross Bar, making certain to catch only the Bottom Thread of the stitch.  Pull the hook forward and then up to the top of the piece (the Twist Up).  This will twist the Bottom Loop up to the top of the piece.  Then, Yo, pull through leaving the new loop on the hook.  Repeat this across to other side, but work the last stitch as you normally would through the Vertical Threads on the end.  Return as you normally would for any other TC stitch.

The Bottom Thread Cross Bar Foundations are difficult to use and, in my opinion, not worth the effort.
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For a diagram of all the various Threads of a Tunisian Crochet Stitch,
Click Here!
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Abbreviations:  
Beg: Beginning
 Ch: Chain stitch   
Lp: Loop  
Hk: Hook
DO: drop off
PU: pick up
Sk: skip stitches
Sl St: slip stitch
Yo: Yarn Over hook
Tks-Knit st  
Tss-Simple/Afghan St Tps-Purl St
 Trs-Reverse St
 Tfs-Full/Plain St

Trps-Reverse Purl st