In most cases, raising a rescuer and/or patient is a last resort, because overcoming gravity requires significantly more effort than lowering. That said, there certainly are times when raising is a better choice than lowering. These include when raising the load a short distance will avoid a very long lower, when your ropes aren't long enough to reach a safe landing, when there are additional hazards below, when the only egress is above you, when communication will be difficult, etc.
The term "mechanical advantage" is a measurement of how much your rope and pulley system will leverage the force that you put into them. For example, without mechanical advantage you would need to pull 100 kg to raise a 100 kg load. That is "1:1" mechanical advantage (pronounced "one-to-one"), because for each unit of force you put into it you will get the same amount of force out.
However, in a "3:1" mechanical advantage system, for each one unit of force you put into it (e.g., one pound or one kilogram), you will get three times that amount of force out of the system. A 3:1 system will let you raise a 100 kg load by pulling 33.3 kg. (You would actually need to pull a little more than one-third due to friction.)
RopeRescueTraining.com provides details on 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, and 9:1 systems, although the most common systems used by rescuers are 1:1, 3:1, 5:1, and occasionally 9:1.
(The following pages explain how to create various mechanical advantage systems, but you can also jump to the section about calculating mechanical advantage.)
The "critical point test" (aka "scissors test") requires that if any one item fails, nobody should be injured.
A "bend" is a knot that joins two ropes.
A "hitch" is a type of knot that must be tied around another object.
The "whistle test" requires that if all rescuers let go, nobody should be injured.