Rope is made from fibers twisted or woven together. Generally falling into two categories, natural and synthetic. Some natural fibers used are cotton, sisal, manila, and where people are trusted not to try to smoke it, hemp. Synthetic ropes are mostly Dacron®, nylon, polyethylene and polypropylene.
Unless they are braided, common ropes are made by twisting fibers (usually) to the right into lengths called yarns. Yarns are then twisted together to the left and called strands. Strands are twisted together to the right.
Most braided rope has a woven shell surrounding a core of fibers. It is more flexible and has less stretch than twisted rope.
When the strands are twisted to the right, it is said to be "laid" right-handed. So heavy rope laid this way should be coiled in a clockwise (left to right) manner. It is these twists in rope that give most knots their gripping power. So, a knot that works well with rope may slip apart when tied with a smooth monofilament fishing line.
When a knot is tied, fibers become bent, stretched, squeezed and broken. This weakens the strength of the rope, knots may be rated by percentages of how much havoc they cause on the overall strength of the rope. Some knots weaken a rope by 20%, some 50%. Add to this the age and the amount of use the rope has seen. For this reason, the rope and knots used for climbing have to be chosen with care.
Overhand - Overhand Loop
It doesn't get more basic than the overhand (thumb knot). It doesn't have much use other than a stopper knot.
It is difficult to untie and weakens the rope. But it is the foundation of many other knots that you will find useful.
An overhand loop, or loop knot, is the simplest fixed loop you can tie. Like the overhand above, it is very difficult to untie.
You can use a variation of this to tie two lengths together, instead of doubling up one line, hold two lines together, and tie both as if one line, and form an "X" or a "Y" they will not come apart or slip. If you pass the doubled up end through the eye of the loop a second time, you will form a "surgeons loop" that is slightly stronger.
Reef Knot, Half and Double Hitch
The reef, or square knot is a classic, used by sailors to bunch up sails, also for tying up your karate belt. It is used for tying two lines to bind things together. It is easy to tie, untie and adjust.
Another way to tie this is tie two ends together as an overhand, then tie the two ends together a second time. When tied properly, the two ends will exit from the same side. If tied improperly, you will get a Granny knot.
A half hitch is a common way to end off many knots. Here is a single, followed by a double, half hitch. This will loosen and slide under use, when strained from different directions.
Figure of Eight, Bowline
These two are similar in function to the overhand and overhand loop, and represent the next level up.
Figure of eight, another stopper knot, is larger than the overhand. It can be tied and untied and has less impact on the overall strength of the rope. You can double up a length of line and tie a figure eight and produce a better all around fixed loop.
Bowline is the most widely used fixed loop. Much of the language of sailing and knotting is influenced by the slang of British sailors. "Main sail" is pronounced "mains" etc. The correct way to say it is bo-lun'. The bowline is easy to tie, untie and strong.
Anchor Bend, Fisherman's Knot
Anchor Bend is really a hitch. Note the similarity to it and the double half hitch above. Slipping the working end through the turn locks the knot in place, preventing it from sliding. For tying a line around a spar, I find using an extra round turn so that there is one on both sides of the standing part, even holds it in place better.
Trilene, Surgeons Knot
The trilene was developed by the company that makes the fishing line. It's about the best knot for tying a monofilament line onto a hook or lure.
TIP: Monofilament line should be moistened before closing the knot to keep down friction heat that can weaken the line.
The surgeons knot is used to tie two lengths of monofilament line together. Note that one end will have to be worked through the loop. So, if you are tying two long lengths together, the end that will be worked through the loop should be wound around something or left on a spool. The loop made in this case should be large enough to pass it through the eye.