K4
The K4 Method was created by Thom Barlow (a link to his guide on his website is provided after this summary). This method takes advantage of four unsolved adjacent centers to pair up three dedges of the first layer and then, once the remaining four centers are solved without destroying the 1X3X4 block initially formed, it uses various commutators to directly solve the remaining winged edges in the first three layers as well as the last layer.
One of the biggest challenges of this method is to master solving the last layer. One can easily solve the last-layer corners using COLL or regular 3X3X3 corner solving methods, but solving the last-layer dedges requires commutators. Thom Barlow covers this portion of the method in "Step 7" of his guide. He has provided an algorithm for each of the 28 possible cases for moving three winged edges at a time (3-cycles) as well as parity algorithms and 2 2-cycle algorithms ("permutation parity").
With 28 different possible cases just for 3-cycles, solving the last layer can be overwhelming. However, memorizing all 28 cases is not a prerequisite for being able to solve the last-layer dedges with confidence: only a handful of commutators is required because one can use variations of those to attack any of the 28 cases by adding necessary preliminary moves to those commutators (and undoing them after the commutator is complete).
For convenience, member cmowla has made a complete table of all 28 3-cycle cases for the last layer, each accompanied by Thom Barlow's algorithm for that specific case.
File:K4LL3cyc1.PNG File:K4LL3cyc2.PNG
For theory on why there are exactly 28 3-cycle cases, visit this page [1]. (In that thread, there is also discussion on the number of cases for higher order cycles as well, such as 4-cycles, 6-cycles, 8-cycles, etc., and multiples of lower cycles, such as 2 2-cycles).
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