Rope material comes in two categories:
Natural and Synthetic.
Natural rope primarily refers to manila hemp rope, an older standard. Many old theaters still have hemp ropes around somewhere. It was very sturdy, but very hard on the hands, and highly susceptible to changes in temperature and moisture.
Synthetic ropes come in nylon, polyester and polypropylene.
Nylon - strongest, but stretchy and heavy
Polyester - nearly as strong, not stretchy but a little heavier
Polypropylene - Light weight, not as strong but generally strong enough for stage purposes, a little slippery
Construction of ropes can be:
Twisted into yarns - not easy to hold
Braided - strong and easy to hold
Hollow braid - no core, not too strong but inexpensive
Kernmantle - braided around a sold core, strong and smooth
Double braid - braid around another braid, very strong, heavy
Knots for the Stage
There are hundreds of kinds of knots out there, but there is a handful that every stage hand should know well.
The first and foremost is the Drop Knot. This one is useful for tying up drops onto a batten, tying up cables, etc. And if you know how to tie your shoes, you already know this knot.
The Clove Hitch is very useful for theater because you can use it to pick up a pipe with two ropes, attach a line to a batten, secure a line to loom of cables, etc. It is most commonly used for cable pick lines. It will remain cinched tight as long as there is weight on it.
When the weight comes off of it, the knot can loosen, so it is best to secure it with a Half Hitch.
A clove hitch is also useful because it can be easily adjusted to change the length of the line you are using. This means you can hang a pipe from two or more lines, and then easily level the pipe using your knots. You can also create the knot, and slip the pipe through it. All of this is demonstrated in this video.
The Bowline knot is extremely versatile and very sturdy. The more weight you put on a bowline knot, the stronger it is (within the limits of rope strength).
It allows you to create a loop of any size around a load. This loop, once tightened, will stay this size. We use it in rigging, because anything with a solid loop (such as a shackle) can be lifted into the air securely.
The other handy thing about using it for rigging, is that the size of loop can be tied based on what the up-rigger needs. And although it will not untie itself, it is easy to untie using the little "lever" that is made at the top of the knot.
Always take a last look at the bowline (or any knot) before sending a load up on it.
Securing to a Pin
A Belaying Pin knot is used on the pin rail for securing cable picks and other pulley lines.
A pin-rail has a long rail with holes in it that the belaying pins fin into. The pins can be shifted around as needed.
Primarily, the knot just involves wrapping the pin with the rope in a figure-8 pattern 2 or 3 times and then securing it at the end. The friction of even one wrap helps make adjustments to fine tune the height of what you are lifting.
The Prusik or Sunday
The Prusik knot is a climbing knot that involves tying a bite of a line to another rope. Climbers can actually use this knot as a ascender.
The prusik is used occasionally in stage work to breast a line in one direction, in order to get that line out of the way of a process.
It is a very simple knot, primarily just a double choke made from a loop.