Byzantine weave is great weave to start with as it is not a very complicated weave, but works well for bracelets and necklaces. It gives a complex impression but goes together easily with a wide variety of ring sizes.
Stainless Steel 18g 3/16" ID
Note: With most weaves in chainmail there are a variety of ways to put the rings together. This is just how I find it easiest to create this weave. If you find a way that is more suited to you, or the size of the ring you are working with, do what you find is personally the best.
To start this weave, use 10 rings, opening 4 and closing 6.
Using 4 closed rings and 1 open ring, create 1 four-block.
Add a second open ring to the four block created in Step 2.
Connect the remaining 2 closed rings to the block using one of the remaining open rings.
Add the remaining open ring to the same location that the last ring was inserted creating a row of 2X2X2X2X2
Stretch out the 2X2X2X2X2 and choose 1 end to continue the pattern.
Fold the 2 end rings back.
Add 2 rings to the bottoms of the rings folded back in Step 7.
Add 2 more rings to the 2 rings added in Step 8.
Add 2 more rings to the 2 rings added in step 9.
Fold the 2 end rings back.
Add 2 rings to the bottoms of the rings folded back in Step 11.
Add 2 more rings to the 2 rings added in Step 12.
Add 2 more rings to the 2 rings added in Step 13.
Fold the 2 end rings back.
Continue Steps 12-15 over and over until the chain reaches the desired length. With the basic idea of (Add 2 ring, Add 2 rings, Add 2 rings, fold them back, repeat)