The bowline is a knot that forms a fixed loop at the end of a rope, used by some climbers as an alternative tie-in and to attach the rope to anchors or trees. Its main advantage over the figure-eight is that it unties easily even after heavy loading, but it must be backed up, since an unsecured bowline can shake loose.
A prusik knot is a friction hitch tied with a thin loop of cord around a climbing rope. When weighted it grips the rope and holds; when the load is released it slides freely by hand. This lets climbers ascend a rope, back up a rappel, or build a hauling system for crevasse rescue.
The figure-eight follow-through is the standard knot climbers use to tie the rope into their harness. It is strong, easy to inspect at a glance, and holds securely under load, which is why it is taught as the primary tie-in knot worldwide. Climbers finish it with a backup or stopper knot.
A clove hitch is an adjustable friction knot that climbers tie directly onto a locking carabiner to attach themselves to an anchor. Its key advantage is that the length can be fine-tuned with one hand after tying, without untying the knot, making it the standard way to clip in at a belay station.