Full 3x3 notation tutorial

To allow algorithms to easily be explained, cubers have developed notation to refer to particular moves, for a 3x3, this is all the notation you need:
basic notation:
R - turn the right face up
R' - turn the right face down
L - turn the left face down
L' - turn the left face uo
U - turn the top face to the right
U' - turn the top face to the left
D - turn the bottom face to the left
D' - turn the bottom face to the right
F - turn the front face clockwise
F' - turn the front face anti-clockwise
B - turn the back face anti-clockwise (from your front reference point)
B' - turn the back face clockwise (from your front reference point)

We also have some more advanced notation such as the following:
middle slices:
M - turn the middle slice down
M' - turn the middle slice up
E - turn the equitorial face to the left
E' - turn the equitorial face to the right
S - turn the side slice (imbetween F and B) clockwise
S' - turn the side slice anti-clockwise

Wide turns are denoted by a lower case letter and they refer to turning the middle layer next to it with the layer, for example r means turn the right face up, as well as the middle slice.

Rotations are denoted by x, y and z and represent turns of the whole cube:
x is a rotation of the whole cube in the direction of R, it can also be done as R M' L', whatever is on the front is moved to the top
y is a rotation of the whole cube in the direction of U, it can also be done as U E' D', whatever is on the right is moved to the front
z is a rotation of the whole cube in the direction of F, it can also be done as F S B', whatever is on the top is moved to the right.