This tutorial assumes that you already know how to solve a 4x4, but want to solve it more efficiently.
The first step of the Yau Method is to complete the white and yellow centers. Next, pair three edges of the cross. Start by pairing the white edges and putting them into position. Next, rotate your cube so that the cross is on your left side and the open slot is at the top.
Solving the centers using the Yau Method is done by using the empty slot created by your three edge cross. The empty slot is your working layer to create the centers. You do this by creating lines at the top and only rotating the three right layers.
Form a two long line at the top, then put it on the left of the top center. Then, rotate the inner left layer clockwise. Do this until you have three lines of three centers solved and one empty center at the top remains. Create the other three lines and pair them with the lines you just created. Your centers should be solved.
Finish by pairing the final white edge of the cross.
Finish pairing the edges and then solve the cube like a 3x3.
When on the last layer, there is a chance that you will encounter a parity case. Parity cases are cases that are not possible on the 3x3. Therefore, these cases need special algorithms to solve (x means to rotate the whole cube away from you 90 degrees, and Rr means to rotate only the inner right layer clockwise).
OLL Parity:
PLL Parity:
A collection of various parity cases and alogrithms to solve them.
General tips to help you solve the 4x4 cube.
Review how to solve the 3x3 cube.