Just a Sample of what you’ll find in Encyclopedia of Tunisian Crochet!

Flying Geese Stitches pg 2

Flying Geese #4: Purl Tss2tog/Purl Combo
Worked in multiples of 2 sts +3 chs.
Row 1 Forward and Return: Follow instructions for Tunisian Simple Stitch.
Row 2 Forward: With 1 loop on hook, (Tps2tog, YO,) across the piece, working a Tss into the last two sts. Return.
Row 3 Forward: Work 1 Tps in the vertical and diagonal threads across the side. Return as you normally would.
NOTES: For Row 3 and all other rows, you will work with both the vertical threads and the diagonal threads.
The stitches will look similar to this
|~/~|~/~|~/~|~/~|~/~|~/|
For Rows 3+ you will slip the hook under the vertical thread for the first st, and then slip the hook under the diagonal thread just to the left of it for the next st. Remember to work from the back of the piece, since this is a  Kim and ARNie’s Purl stitch.

Flying Geese #5: Tps2tog
Worked in multiples of 2 sts +3 chs.
Row 1 Forward and Return: As you normally would for any TC st.
Row 2 Forward: With 1 loop on hook, (Tps2tog, YO,) across the piece, working a Tss into the last two sts. Return.
Row 3: Repeat Row 2 Forward and Return.
NOTES- The stitches will look similar to this:  
|~/~|~/~|~/~|~/~|~/~|~/|
For Rows 3+ you will slip the hook under the vertical thread and the diagonal just to the left of it. Yo, pull yarn under those threads and leave the loop on the hook. Yo, and work next st. Remember to work from the back of the piece, since this is a Purl stitch.


Front Crossed & Twisted Tunisian Simple Stitches

Front Crossed Tss-FXTss
This stitch uses the Simple Stitch Foundation, and is formed by skipping a stitch to work a Tss and then crossing in front of the stitch just finished,  to work a Tss in the skipped stitch.
Any number of chs + 2 extra for the edges.
Row 1 Forward and Return: As you normally would for Tss.
Row 2 Forward: Ignore the outer most st. *Sk next st. Tss in following st. Cross in front of loop just formed, and Tss in 2nd st.  Sk 1 st, and Tss in next st. Tss in skipped st.  Repeat from * across side, ending with 1 Tss in end st. Return as you normally would.
NOTE: This stitch is not suitable with the Knit Stitch Foundation.

Front Crossed Double Tunisian Simple Stitch- FXDcTss
Any number of chs + 2 extra for the edges.
Row 1 Forward and Return: As you normally would for Tss.
Row 2 Forward: Sk 2nd st, and work 1 Double Tss in 3rd st. Work 1 Double Tss in 2nd st.  *Sk 1 st, and Double Tss in next st.  Double Tss in skipped st.  Repeat from * across side, ending with 1 Double Tss in end st. Return as you normally would.
NOTE: This stitch is not suitable with the Knit Stitch Foundation.
Twisted Simple Stitch
The mechanics of this stitch are simple once you learn a trick.  The basic principle of this stitch is to use the Simple Stitch Foundation, and twist the vertical thread before you yo, and pull a loop onto the hook. This can be easily done by changing the way in which you insert the hook into the stitch.  
Instead of slipping the very tip hook under the vertical thread from the right, use the actual HOOK to slip under the vertical thread by approaching it from the LEFT. Then turn it all so that the HOOK is facing up.  That will twist the vertical thread, and then yo, and pull a loop onto the hook.
The Return as you normally would.

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Specialty Stitch:
Tps2tog-Purl Stitch 2 together: (This is also known as a Decreasing stitch with a Kim and ARNies Purl Foundation.) Slip hook under 2 Back Vertical threads, Yo, draw yarn through both vertical threads and leave loop on hook. Return as you normally would.