Proper Rope Tying for Rock Climbing

Overview
Rock climbers depend on several basic knots to keep themselves, and their equipment and supplies safe and sound. Depending on your needs, there is a knot suitable for each situation. While these knots are easy to complete in a matter of seconds, for safety's sake it is important to practice these loops multiple times so they are second nature to you when up on the mountain.
FIgure Eight Knot to Join Two Ropes
Fashion a figure eight using the end of one of your two ropes. Lead the end of the second rope parallel with the first. Weave your second rope through the first, following the first rope to make a double figure of eight. The second rope must exit beside the standing end of the first rope. Pull all ends tight. For carrying people, do not use the figure eight knot on ropes of different sizes.
The Klemhest Knot for Rappelling
Fashion one piece of cord into a loop and pass the loop around your main rappelling rope in three complete rotations. Make sure the cord from each rotation is resting neatly on top of the other. Pass the knot through the loop and pull it back down in the direction that you expect to be be pulling when rappelling down the mountain.
Rolling Hitch for Sliding and Gripping
The rolling hitch or taut line hitch secures a rope to another one that is parallel to it. Many prefer it when carrying loads because the rope can be adjusted without needing to be untied. Take your main rope and wrap your second rope around it two times, making sure the laid rope loops are side by side. After completing a third rotation, tuck the end of the rotating rope under the loops snuggled between the first and second rotation. Make sure the end of the rotated rope is poking up and pull this end taut.
Alpine Butterfly Knot
When applied in the center of a rope, the alpine butterfly knot, also referred to as a lineman's knot, allows for strain between the knot and the rope's end. These knots are used to make handles in a rope when you are climbing as part of a rope team. Many like this knot because it can take pulls from either end without coming undone. You will make this knot by wrapping the rope around your hand two times, with the first wrap resting near where your palm meets your thumb and the second around the middle of your fingertips. With your free hand, pick up the turn near your fingertips and wrap it around the others two turns. Pull it through and tighten by pulling on both ends as well as the loop end.
The Overhand Stopper Knot
The overhand stopper knot ensures that the rope does not pass through a pulley or block. Some climbers like to use it in conjunction with other less secure knots, such as the figure eight, to give both knots added strength. To form this stopper knot, wrap the rope's end around itself one time. Thread the top end of the rope through the turn and pull both ends tightly.
Resources
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knots
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ropes
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climb
reference
Proper Rope Tying for Rock Climbing
reference
Animated Knots by Grog
resource
Learn to tie a Prusik Knot for Top Rope Climbing