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I start with a length of waxed polyester thread. It comes in many colours, is relatively inexpensive, very strong, resistant to wear and easy to work with. Polyester melts under heat, so the end of the thread can be conveniently shaped (e.g. flat to slide in a needle's eye or in a thin rod to string a bead). I have been using waxed polyester for leather stitching (handsewing) for years and it never let me down.
Craft shops hold threaded barrel clasps for bracelets, necklaces etc. When properly screwed-in, they are quite reliable. Made from brass alloy, they usually come in silver and gold colour. Typically, on their "outside" extremities they present wire loops (or "grommets") to attach a thread or wire.
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Each bracelet has seven or nine thread runs (each approx. 16 cm long, for a typical female wrist), i.e. three- or four- and-a-half loops of thread around the clasps' grommets. An odd number of strands means that threading finishes on opposite ends of the bracelet. The rest of the thread is then used to tie the loops together (e.g. with a couple of half-hitches around the bunch).