This small i guess small instructable will cover a few basic weaves some intermediate and a advanced or two.

Critical things you need to have and know before starting.
One: Tools, You will need pliers to open and close rings
Two: The Color Key, this key is used throught this instructable

Red: The ring(s) to weave thru.
Blue: The inactive or finished parts of a weave.
Green: the active or unclosed ring you are weaveing into the mesh/chain
Yellow: Orbital captive or pre closed ring.
Purple: Rubber or flexable ring.

Aspect Ratio: is a number driven from the difrance between the rings inner diameter and the wire diameter. we use this number to get a ring size that will work for a given weave. For example, If you want to make Byz you would use a AR or around 3.5 this means if you want to use 0.032 wire you simply multiply the wire size by the AR, 0.032 * 3.5 = 0.112, this tell you that your ID = 0.112. Another example, Say you have 0.25 mandrel for your ID but don't know what wire to use to get AR 3.5. so you divide the 0.25 by the AR of 3.5 this will give you 0.071. now say you made a awesome weave and what to share it with every one and you don't know that AR, well that easy, Divide the ID by the Wire diameter. ID 0.125 WD 0.032 = AR 3.9 One of the more amazing bonus of this added math is that it alows you to scale up or down a weave as well if you know the ID you want to get approximate size say 0.5 wide pice of BB2B and know that it is 4 rings wide you know already that 0.125 is going to be close to ideal ID you just need the wire size. ID 0.125 / AR 3.9 = WD 0.32. now say you don't like that size. and want it more belt sized say around 2in wide. you take your 0.5 ID divide it again by the 3.9 AR and you get a wire size of 0.128. So in summery the Formulas

ID / WD = AR
WD * AR = ID
ID / AR = WD

What weaves are here?

Euro 4in1 unbalanced aka Oops
Byzee Beez to Buterflies
Butterfly
Candy Cain Cord
Celtic Filagree
Fluer De Lis
Celtic Cross
Celtic Dawn
Conundrome
Berjao Flowers
Firemens Hold Link 4
Daisy Chain
Elfen Tracks

That should about cover the introduction, Lets get to weaving shall we.

Step 1: Brejao Flowers

This is a fun weave with a nice sheet form making it useful for clothes bags draperies, and many other normally cloth forms.

AR 6.0 +

Step One: Begin with Two 2 in 1 chain of equal length, you may make more than two to start these chain are used to determine the pieces starting length.

Step two: Now Add a ring between the lowest two rings as shown, you will continue this every two rings up the chain forming 3 ring mobi all the way up, you will want to do this to both chains. At this stage it may be helpful to not get the rings all moved about, you can pass a rod or stiff string thru the center of the mobi units to prevent over tangling.

Step three: Lay at least two chains net to each other and in the mobi you formed at the bottom of the first chain add a ring to the out side of the mobi, then pass it thru the eye of the mobi of the second chain making it not a 4 ring mobi unit. again you will continue this up the chain every unit.

Step Four: To finish of the first chain just add the 4th ring to the mobi units and continue adding 3 ring mobi chains until your size is accomplished.

Thats all there is to it.

Step 2: Butterfly Chain

This weave uses two ring sizes the smaller rings having a AR of 3.9 and the Larger rings having a AR of 5.

Step One: Make a few mobi out of the AR 5 ring I used three rings per mobius.

Step Two: Weave on 4 AR 3.9 ID rings onto the mass.

Step Three: Now we are going to split it up a bit. Weave one ring onto each of two rings splitting the four stack.

Step Four: Split the two new sections and weave in two rings, one on top and one on bottom, using one ring from each group.

Step Five: Repeat the other steps 2-4 on the opposing side of the Mobi this completes a single unit of the weave, make several of these before you continue.

Step Six: Now lets connect a few sections. Gather two sections and weave in a ring through the bottom three rings on the outer ends of both sections like so.

Step seven: Repeat the above in mirror for the top.

Step Eight: Repeat repeat

Step 3: Byzee Beez to Buterflies

Love this weave easy Byz variation and good looking to boot.

AR 3.9

Step One: Open six rings and close six rings.
Step Two: Add four closed rings to one opened one.
Step Three: Close ring and add a second one through the same four rings as the first.
Step Four: Arrange in a 2 in 2 chain and add one more section of 4 rings.
Step Five: Rearrange the rings as if you were to make Byzantine.
Step Six: Make a second piece just as the first and connect where shown.
Step Seven: Don't forget to add the bottom.
Step Eight: Continue Steps One to Seven until you have what you need, and you are done.

Step 4: Captive Zen

I'm not going to give AR for this one as with this many ring sizes it makes it a little harder to work out

Ring size for this weave you will need three ring sizes each smaller then the next.

smallest ring 18g .173 ID (4.4mm)
Middle Ring 18g .236 (6.0mm)
Largest Ring 18g .279 (7.1mm)

Okay lets get weaving this.

First make a 2 in 1 orbital section, do this by weaving a 2in1 chain from the smallest rings and using the middle size as the orbital ring. you will want to make a few of these sections before continuing.Now using two of the section you made in the last step weave in the largest ring on either side of the small ring in the center through the mid sized rings. It should look like this when done.Adjust so that the top and bottom small rings look like this.Next weave in two more small rings using the right top of the left section, left top of the right section, lower right bottom of the left section, and lower left bottom of the right section (that's hard to say) or see pic above. Continue steps 2-4 to make the chain form of the weave.Using the same methods you can make the sheet variation of this weave but duplicating the form at 90 degrees. Like above.Good luck and have fun.

Step 5: Candy Cain Cord

AR 4.7

okay this is one of those weaves that is unstable at the start so i've have chosen to use a starter weave. in this case the base weave. Full Persain 6in1 , you need only a section 4-5 units long to get it going and something to hold on to.
OKay now that you have that. lets get to weaving. add your firt ring on th bottom eye like shown.

Flip the section 180 and do the same to the back side.

now give the section a 90 turn to one side and pass you new ring thr the eye and you first two rings.

Flip and repeat.

at this piont you are back to step one but lets run thru it again. toss a ring around the bottom eye.

flip and repeat.

back to step 4-5 rotate 90 and add your ring around the eye and thru you prior two rings.

Flip and repeat.

Now that you have the idea, run out a few more section.

Dissconnect your starter adn you are done.

Step 6: Celtic Cross

ARs 4.6 and 4.3

Step One: Start with a piece of Celtic Visions.
Step Two: Add a Ring here, in between the two Celtic Visions sections.
Step Three: Pull in two rings one from each side of the visions and use a 1/4 ring to connect all three rings.
Step Four: Repeat on othr side.
Step Five: Jump over two sections and do steps 2-4 again.Step six: Keep doing this and you will complete it

Step 7: Celtic Dawn

Start with a pice of Helm chain, now you need some AR 4 rings.

Weave the rings in a 1 -2- 1-2 pattern ware the 2 is in the single ring of the helm pattern.

Next fold in one ring from each of the bi-rings and link them together with a new ring.

repeat on oposing side and continue down the chain. nice and simple.

Step 8: Celtic Filagre

Again the amount of rige sizes make ARs difficult so none are given.

Sizes : 16awg/7.75mm, 16awg/4.75mm, 18awg/4.5mm, and 20awg/3.25mm.

Lets get weaving.

Start by making a 2 in 2 chain from one small and one medium ring by placing one medium and one small ring around them.I know that first step is kinda confusing but continue that pattern until you have 8 sections like this. Be sure to keep the medium rings on the one side. If you get the rings all mixed this trick will not work.Now loop them around in a circle and connect them the in the same way with all the medium rings facing the inside of the loop.Now all we have to do is weave in the largest ring through all the medium rings on the inside.There that is a complete section of it. Now we move on to connecting two sections together. A simple 2in2 will work just fine. Use the small rings for this.Continue doing this until you are satisfied with it.

Step 9: Daisy Chain

Daisy Chain Some times call Chrysanthemum.

Two sizes, Large rings and small rings AR of large ring must be a factor of the small ring. this will help make the final circle of rings stiffer. ar of around 10 and a AR of 3.8 seems to work well.

This is a simple weave FILL the large ring about 2/3 full of rings. then add a outside layer of rings in a 4in1 pattern style (thru the eye manor) make a few of these units, then using two rings connect them to one another.

Step 10: Elvin Tracks

AR 5.4

Diving right in, start with two 2 in 1 chains of equal length.
Step Two: We need to line them up together like so:
Step Three: Count in two “eyes” and pass your ring through both eyes in the second section and around through the top on the first like so.
Step Four: Mirror this on the opposing side of the chains, moving one eye set forward.
Step Five: Repeat, Repeat, DO IT AGAIN!

Okay Variation 2, Restarting with your 2 in 1 chains this time instead of starting off in the second eye start off in the first. HUH I can hear you saying. Because the two chains are mirrored this will create a different outcome of the chain.

Step 11: Euro 4in1 Unbalanced

AR 4 +

This weave is known by a few names, European 4 in 1 Unbalanced being the most used. Also called Oops and Reversing Bias 4 in 1.

Oops is a misleading name. E4in1U is not an easy weave to start. It is true that once started it simple enough to do. So I’m going to show you how to use a starter weave to get it going, then will unweave or disconnect the “starter” and continue with this weave. Since this weave is 4in1 we'll start with a European 4 in 1 base section. It best to use a small section but still big enough that it will give you a well supported starting piece before you disconnect it. I recommend that you use a piece that is 5x3. Go ahead and make it from AR 4 this will make it nice and thick, and this weave looks best thick Now that you have that done lets change it over to the new weave

Step one: Turn the weave 90 degrees. Now add a new ring through the top 3 rings.
Step two: Do the same for the bottom three rings.
Step Three: Link in a ring through the top ring in the “starter”.
Step Four: Weave one into the Center of the two 3in1 rings but pass it through only one ring.
Step Five: Do we need a step five lets skip to six…hehe.
Step Six: Do the same linking as in step Three.
Step Seven: Now we have the connections and they will not move on us we start the fun. Using a single ring, weave it through 3 of the top new rings.
Step Eight: Now do this again for the bottom three rings.
Step Nine: Do the same as you did for Steps 3 through 6.
Step Ten: Repeat Steps Seven through Nine until you have a strip a few inches long.
Step Eleven: Now that it is a good size we can remove the 4in1 starter from the end.
Step Twelve: this part can be hard to see sometimes due to the confusing nature of the weave. But you add just one ring through just one ring, best way to see where the one ring goes is to look for that 3in1 section that it will complete and in doing so makes the pass through ring 4in1. Here I have added all of them for this section.
Step Thirteen: Now for a Closer look and the next ring. Using two of the 1in1 rings add a new one as shown it will be 3in1.
Step Fourteen: Do the same one section down, remember that it is 3in1
Step Fifteen: Continue to do step 13-14 all the way down the piece.
Step Sixteen: Now we have to reverse the connection but keep the flow. Do this by adding another set of 1in1, be sure they complete groups of 4in1. Note the yellow ring here, it's floating in mid space. This is a ring that you will have to add later. Keep in mind that the off row will always need this seemingly extra ring to complete it.
Step Seventeen: Here we are adding a New ring to the end ring it is 2 in 1 despite missing the red ring from the 1in1 from the previous step (my bad there).
Step Seventeen: Now we do the reverse of step 13 but still doing 3in1.
Step Eighteen: Continue step 17 until you get to the end, at the last section add the yellow ring onto the new one being added, this will stop the weave from contracting on you.
Step Nineteen: Continue doing steps 13-19 until you have what you like.

Step 12: Firemans Hold 4

AR 4.8

Step one: Close a few rings
Step Two: Hold one ring on while placing another through and locking it in a orbital form like so.
Step three: Add a ring off the orbital ring like so
Step Four: Add in a locking ring through the locking ring from step two and intersecting it with the ring from step three.
Step Five: Now we are repeating steps three......
Step Six: Now we are going to connect the two sides and complete the form. Add one ring to the two rings indicated here.
Step Seven: Final ring placement is nothing more then step three again but going through both rings on this side instead of just the one.Done Finished!!

Step 13: Fleur De Lis

AR 3.9

First Step: Make a two in three chain section.
Step Two: You'll want to make a few of these section before we move on.
Step Three: Now we have to pull out the center ring in the three so that it look like so. you may hold it to make thing easier.
Step Four: now with the ring you pulled forward and the two ring you did not on another section add a ring to each side.
Step Five: Continue doing this until completed length is reached.

Step 14: Halo

No it not the game!

Step one: Gather your rings. ARs are 6, 5, 4, and 3.
Step two: Start by linking two AR4 rings with an AR3 ring to make a 2in1 section.
Step three: Place two AR6 rings as shown.
Step four: Now add two AR5 Rings through the AR6 but around the AR4 rings.
Step five: Repeat this on the other side so that this unit is stable and you can set it down. Make another of these sections before proceeding to step 6.
Step six: Take the two units you made in step 5 and weave a set of AR6 rings through the AR5 rings, one on top and one on bottom of the AR4 ring.
Step seven: Continue making sections and linking them to reach the length you would like. In short... done!..:P

Step 15: Hoodoo Hex Sheet

AR 3.5

Okay first thing you need to make some 2in1 chains. make 4-5 to get started with. now lay two of them down so yu can see there alinments. and arange them so that the tops and bottoms alternate and face each other in to opsing chain. what done that mean?.well just look at this. you may need to re-aline this every time you add a new ring untill it stabilizes.
Now we add the first rings, skip the end ring and pass you first ring thru the eye of the next two rings on both chains.

set it down and realine if you need to. Next jump the next eye and use the one after it and do the same as previose step.

Again...

and i think you get it, finish out the cain.

Now grab another 2in1 chain and aline it like so.

Now we go back to step 2 but don't skip the first eye, use it.

same as b4 now, skip an eye and use the second one.

And again..

Finish out the chain.

Continue this method of alternating alignments and alternating eyes to complete the hight of the chain.