Waterman method

The Waterman method is a method for solving the 3x3x3 cube which was invented by Marc Waterman in the 1980s. The method is based on Corners First methods but is efficient enough to be used for advanced speedsolving.
History
The method was developed by Marc Waterman and his friend Daan Krammer in 1981. Marc added "a lot of additional processes and shortcuts" to achieve a sub17second average by the mid1980s (Minh Thai's 1982 "world record" by comparison was 22.95 seconds). The method seems to have been littleknown however. When cubing revived in the late 1990s Jessica Fridrich put her algorithms on her webpage leading to the rise of CFOP as a main speedcubing method. Although many websites mentioned the Waterman Method, its details were nowhere to be found.[1] In August 2004 Josef Jelínek contacted Marc Waterman[2] and obtained information about the method which he placed on his rubikscube.info website.
Classification
It has occasionally been questioned as to whether the Waterman method is a pure Corners First method. According to Josef Jelínek:[3]
Waterman's method can be considered pure Cornersfirst. The main reason for that is that you can solve all corners first before starting solving edges without any change to the sequences used or a method itself except for swapping two steps. The reason Marc solved one layer completely first was probably because he was used to do it like that. It is sometimes (often) easy to see how to put some edges (and a center) to the first layer during completing the first four corners, so reducing the number of turns required for the first layer. CLL sequences used preserve the first layer. Personally, I solve all corners first + some obvious edges of the first layer.
Steps
The steps are as follows:
1. Solve one layer of the cube minus one edge. The original way to do this is by first putting together the corners and then solving the center and edges together. This can also be done with block building (start with a 1x2x3 block as with Roux and then fill in the last two corners). For optimal solving, this layer should be held on the L face with the LU edge empty
2. Solve the corners of the opposite layer. This should be solved using a modified CLL, called WCLL, that has 42 cases and solves the R corners while ignoring the Mslice and the LU edge.
3a. In one of 110120 algorithmm, solve the LU edge, while solving any two R edges. This can also be done intuitively, though it is less efficient.
3b. Finish the R edges while orienting the M edges, all in one algorithm. This step is difficult to learn and has 224 algorithms, but the algorithms mostly use only M, R, r, and U moves, so this is a fast step.
3c. Solve the M edges. This is identical to the 4c step in Roux
Variants
WaterRoux: The first block is solved as in Roux, then the remaining corners are solved in two steps. A ERL algorithm is then used to solve two R edges, and the cube can then be completed with L7E
WaterZZ: Edge orientation is completed while solving a 2x2 block, then a 2x2x3 block is finished in the back, and the FL pair is solved. The cube can then be solved by using one of 614 L5CO algorithms, followed by one of 95 L6EP algorithms.
Simplified Waterman: The first two steps are identical to the official method, but the Last 9 edges are solve in a different way. First, two R edges are solved intuitively, then the last R edge and the LU edge are solved together. An algorithm to solve the RU edge while orienting the M edges is then used, followed by step 3c like above.
First layer on bottom: Originally this is what was used. The first layer  1 edge is solved on the bottom, then normal CLL is used followed by a z rotation.
Full first layer: This was the original method proposed by Marc Waterman. The entire first layer is solved on the bottom, then CLL is used to solve the corners, followed by a z rotation. Two R edges are then solved at once while placing another anywhere in the R layer, and 1 alg is used to finish the R layer while orienting the M edges. Then step 3c can be used like above.
WEG: This method is identical to the main one, but the two edges in the first layer with no edge in between can be swapped. Then WEG1 and WCLL can be used to solve the corners, and step 3 is identical.
RedKB's corners first: The first layer  1 edge is solved on the bottom, then CLL is used to complete the corners. A z rotation is used, then the L edge and the R edges are all solved intuitively, followed by 1 algorithm to orient the M slice edges. Step 3c can then be applied.