Here we sum up the essential you have to know about the 4x4x4 cube to understand the tutorials.
Faces
They are the surfaces containing 16 stickers. There are 6 faces
Center pieces
They are the group of pieces whose colour determines the colour of the whole face. There are 6 centers, and each one contains 4 stickers.
Inner layers
They are called the same way than the faces but with lower case.
Edges
They are the pieces containing 2 stickers. There are 24 edge pieces.
Corners
They are the pieces containing 3 stickers. There are 8 corner pieces
The blue arrow indicates clockwise direction. When we do this movement we write the letter of the layer.
Example: U
The yellow arrow indicates counterclockwise direction. When we do this movement we write the letter of the layer and an apostrophe.
Example: L'
Another important case is the double turn, we turn this layer twice.
Example: D2
In the Case 1 we have the turn of the inner layer. It is the same case that outer layer; however we write the letter in lowercase.
Examples:
Clockwise direction: d
Counterclockwise direction: d'
Double turn (180º): d2
In Case 2 we have the turn of the inner and outer layers. We can turn together the inner and outer layers, with the letter of the outer and inner layers between parenthesis.
Examples:
Clockwise direction: (Dd)
Counterclockwise direction: (Dd)'
Double turn(180º): (Dd)2
The blue arrow indicates clockwise direction in the three axes. When the rotation is clockwise we write the letter of the axis.
Example: x
The yellow arrow indicates a counterclockwise direction. When the rotation is counterclockwise we write the letter of the axis and an apostrophe.
Example: y'
When the rotation is double we write the letter of the axis and 2 after that.
Example: z2