The figure-8 knot — sometimes called the "savoy knot" or "Flemish knot" — is one of the most fundamental knots in climbing. On its own it is a stopper knot, useful at the end of a rope to keep the rope from passing through a belay device, descender, or pulley. Its real fame comes as the foundation for the figure-8 follow-through, the climbing tie-in knot used by virtually every gym and instructor in the world.
The shape resembles the number 8: the rope crosses over itself twice, forming two stacked loops. When loaded, the knot is easy to inspect — both loops should be cleanly stacked with no twists. After heavy loading the figure-8 can be difficult to untie compared to a bowline, but the easy inspection makes it the safer choice for beginners and the gym-standard tie-in.
Learning the standalone figure-8 first makes learning the figure-8 follow-through (where the rope is threaded back through the knot to attach to the harness) much easier. Most climbing instruction starts here.