Square Knot. The square knot is great for tightening a rope around something bulky, as when wrapping a package. It can be used for tying two ropes together, but isn't completely reliable for that application; see the double sheet bend, below. (The square knot is also known as the reef knot.)
Double Bowline. A double bowline lets you tie a loop in the end of a line that won't slip. A noose is fine for many situations, but if you're hauling a person up out of a pit, for example, they'll appreciate not having the loop tighten around their body. Use this knot any time you want to tie a loop that won't cinch tight around a tree, person, climbing ring, etc. (This is a more secure version of a standard bowline.)
Adjustable Grip Hitch. This versatile knot is used to create a knot that can slide freely along a line, but grasps the line when pulled taut. It is useful for stretching hammocks or erecting tents, to adjust the tension on the lines connecting the tent material to an anchor point such as a peg driven into the ground. It can also be used in climbing: (1) as one climbs, the adjustable grip hitch is moved up or down the line; should the climber fall, the hitch cinches up and catches the climber; or (2) Use a couple of lengths of rope as stirrups attached to a line with adjustable grip hitches, then alternately stand on one stirrup while sliding the hitch along the line for the other stirrup. The adjustable grip hitch is also useful for adjusting the tension on line tying down a cargo. (This is a more effective version of a taut-line hitch.)
Trucker's Knot. The best knot to secure that cargo--that lets you pull the line tight and keep it tight--is the quick-release trucker's knot.
Alpine Butterfly Knot. Use the alpine butterfly to create a fixed loop in a length of rope, to use as an attachment point for other lines or from which to hang something, or for using rope as block and tackle.
Double Sheet Bend. Use a double sheet bend to tie two ropes together, even if they are of different diameters. Murphy's law tells us that no matter how long your rope, it's not long enough; the double sheet bend lets you extend your line by adding another length to it. The double sheet bend can also be used to tie a line to something like a metal ring; consider the ring or eyelet the larger of the lines. (This is a more secure version of a sheet bend.)
Sheepshank. The sheepshank addresses another result of Murphy's law: a rope that is too long, or that has a weak point. One could cut the rope to length, or cut out the weak point, but what if one wants to preserve the rope's original length for future use? A sheepshank literally ties up some of the rope at some point between the ends, drawing them closer to one another for a shorter line. A weak point on the rope can be tied into the middle of a sheepshank such that none of the force on the line is applied to the weak point.
An easy and reliable fishhook knot.
In order to keep things simple, I've limited my list of essential knots to just these eight; I figure most of us will figure out ways to kludge together work-arounds for lashings, constricting knots, nooses, and the like. What did I miss that you would consider essential? Let me know if your comments please, and provide a link to a Youtube how-to video.
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