Figure-of-Eight
The Figure-of-Eight knot is probably the most useful of all climbing knots. It is easy to tie, easy to undo after a load has been applied, and puts the least stress on the rope when tied tight. It can be tied anywhere in the rope, but if it's near the end, it should be secured with a stopper knot to prevent the knot from un-doing itself.  There are generally two methods used to tie a figure of eight knot. The first method is used when a piece of equipment is clipped into the loop, the second when the knot is used to tie into something, for example, a climbing harness. 

Figure-of-Eight loop
  

Figure-of-Eight re-threaded
   

The above re-threaded method is usually used to tie into a harness, and is just a case of making a figure-of-eight on the single rope, looping through the harness, and following the knot back through itself. 

Bowline   
The bowline is easy to adjust and untie. Beware, though, that if tied incorrectly in can be unsafe. You should really tie a stopper knot in the loop with the loose end to prevent it from pulling through. 

Clove Hitch   

  
The clove hitch is easily adjusted when place, but is not a particularly strong knot. If one side of the knot is to be loaded, place the diagonal underneath. If both sides are to be loaded, place the diagonal at the top. Tighten before loading, as it may run if loaded when loose. 

Highwayman's Hitch
   
This knot can bear one's weight on one strand of the rope and can be untied by just pulling on the other strand. End 'B' is the load-bearing end. NOT RECOMMENDED for climbing, but excellent for robbing stagecoaches, when you want to get away quick with your rope. 

Fisherman's Knot
 
Probably the simplest knot for joining two ends of rope. Consists of two overhand knots. 

Double Fisherman's Knot
  
Better than the Fisherman's Knot, this uses two double overhand knots. Good knot, as it can be difficult to untie. Check regularly for the loose ends getting shorter, and if so, re-tie. Tighten with body weight. 

Lark's Foot
 
Quick knot, but weak. Best avoided. 

Overhand Knot
 
Probably the simplest knot in existence. Usually used as a stopper knot, but a double overhand is preferable. 

Double Overhand Knot
 
Better as a stopper knot than the Overhand, as it is less likely to pull through. 

Overhand Loop

This is the simplest way to create a closed loop in the middle of a rope. Difficult to untie after loading. 

Sheet Bend

Occasionaly used to join the ends of ropes, may be adjusted easily, but can also come undone easily. 

Tape Knot

Usually used for joing the ends of tapes or slings. Can work loose sometimes, so check regularly, and re-tie if the ends are getting shorter. Tighten with body weight before use. 

Ascending Knots Five ascending knots are shown in all, each have their advantages and disadvantages. Try them all out, and see which you prefer. 

Prusik Loop

The Kleimheist

The Hedden Knot, also known as Kreutzklem First published in 1960 in Summit Magazine. In 1964, the name Kreutzklem was attached to it by someone in the German mountain troops who was shown it by an officer serving in the US Air Force. The Kreutzklem name (cross-clamp) was applied because the original inventor (Chet Hedden) got lost somewhere along the way when it was shown to different people in Europe. 

The French Prusik

The Bachmann