Resistor
What they look like:

How they are shown on circuit diagrams

Their purpose
Resistors, as their name suggests, restrict the flow of electricity. Restricting the flow of electricity is important for a number of purposes including:
How to identify them
Resistor values are measured in
OHM's -
The greater the value of resistance, the less current the resistor will allow to flow ie. a 10 ohm resistor will allow 10 times the current of a 100 ohm resistor.
Values of resistance can vary from tenths of ohms to millions of ohms and therefore the Sceintific Notation system is used to describe their value:
Ohm Single ohm
or R
Kilo Ohm 1000 ohm K
or K
Mega Ohm 1000 000 ohm M
or M
Refer Component Naming Conventions
Due to the small size of most resistors, a colour code is used to identify their value. The code is described below, note that some resistors have 4 colour bands and some have 5 colour bands.
All resistors have a tolerance which describes how accurately the resistor has been manufactured.
In most cases a 5% tolerance is acceptable and only highly tuned circuits require the use of the lower tolerance (more accurate) resistors.

Combination of Resistors
Resistors can be connected in two ways, serial and parallel:
Serial

In the above schematic, two resistors are connected in serial (one after the other) fashion at point B. The total resistance measured from A to C is the sum of the two resistors ie. 56K + 22K = 78K.

Any number of resistors can be connected in this way ie. the total resistance is R1+R2+R3+...Rn (where n is the number of resistors).

Parallel

In the above schematic, two resistors are connected in parallel (side by side) fashion at points A & B. The total resistance measured from A to B is calculated by the formula:

For the example above, where a 56K and a 22K are connected in parallel, the total resistance from A to B is:
Rtot = 1 / (1/56000 + 1/22000)
Rtot = 1/ (0.0000178 + 0.0000454)
Rtot = 15795 or 15.8K
Any number of resistors can be connected in this way ie. the total resistance is:

Rn (where n is the number of resistors).
Note that resistors connect in serial have a combined resistance greater than either single resistor while resistors connected in parallel have a combined resistance less than either resistor.
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