You could also also make the outside by knitting or sewing a tube if you wanted. I crocheted them as I thought knitting may be too stretchy and sewn ones would take some refining before they stopped being all wrinkly and untidy looking.
Borromean rings are a knot (in the mathematical sense) where the three rings cannot be separated even though no two rings are linked. Also the space in the centre is in the shape of a Reuleaux triangle - a shape of constant diameter but inconstant radius.
Step 1: Gather tools and materials.
a crochet hook (2.5mm),
a pair of scissors,
a large-eyed needle,
A different weight of yarn can be used as long as it isn't too chunky, but you'll need to adjust your hook size.
I used a different colour for each of the rings, but you could do them all the same, or make each one striped.
Step 2: Cut the tubing.
I wouldn't reccomend any shorter than this as it would be difficult to get the finished rings to lie flat.
I would also not reccomend making them a lot longer as you'd have to crochet for days but if you didn't mind this it would make them easier to assemble.
Step 3: Start to crochet.
Join into a loop with a slipstitch through the first chain after the slip knot.
Do one chain stitch then single crochet into each of the chains in the loop. When you get back around to the first continue with single crochet in a spiral.
Keep crocheting until it's roughly the same length as the tubing, then cut the yarn leaving plenty for sewing the ends together later, and pull through the last crochet loop.
Step 5: Make paper joiners.
Roll it up tightly so that it's about the same diameter as the inside of the tubing and tape it so it doesn't unroll.
Step 6: Join tubing into a circle.
Step 8: Join the sleeve ends.
When done tie off with the tail from the beggining and trim.