This page lives at http://www.ekrohn.com/cubing/roux.html. These instructions are adapted from those given by Kian Mansour on his YouTube channel. They assume White on bottom and Blue on left, and are easier if you are right handed. See notation.html for diagrams of the different moves if you are not familiar with standard cube notation.
The block is a 3x2x1 group of solved cubies positioned on the DL side. Aim for 15 moves or less.
The simple method is to hold the cube with Blue center on left, find the Blue/White edge and position it at DL (the edge at Down Left) with White down.
Move Blue/Red edge to DF (buffer spot), without moving the Blue/White edge a DL (i.e., no L or D moves). Move Blue/Red/White corner to Top layer, avoiding L or D moves. If White is up, use U moves (U, U', or U2) to move the corner to UBR and do R' U R. Do U moves to position the Blue/Red/White corner correctly relative to the Blue/Red edge in the buffer spot. Do M' or M2 to pair the Blue/Red edge with the Blue/Red/White corner so the Blue and Red edges of the two cubies match. Now position the Blue/Red and Blue/Red/White corner. (Note that l = Lw = "wide left".)
Repeat similarly to build the Blue/Orange and Blue/Orange/White pair and position them.
Build the second 3x2x1 block on the DR side without breaking the first block (i.e., avoid L, D, F, and B moves, or quickly undo them).
Find the Green/White edge and position it at DR with White down. Build and position the FR edge and corner.
Repeat similarly to build the Green/Orange and Green/Orange/White pair and position them.
Orient (yellow up) corners and permute (position) them. This is like the Ortega Corners First "Orient Corners" and "Position All Corners" step except slightly fewer cases because the bottom corners are already positioned and oriented. Note that we do not care about Mslice edges or Ulayer edges in this step. Here we tackle the CMLL in two stages; when you are ready to learn more algorithms, see CMLL algorithms .
You want the Ulayer corners all with yellow facing up. You can do this all with the Sune algorithm (possibly multiple times): R U R' U R U2 R' U2 . The Sune algorithm leaves the UFL (Up Front Left) corner in the same orientation, while it twists clockwise the other three corners. The antiSune algorithm is similar: L' U' L U' L' U'2 L U'2 , though it instead leaves the UFR corner untwisted.
View from the Top  View from the Front  Suneonly Algorithms  More Algorithms 

Learn this pattern (called Mu, or μ) and the algorithm (called
"Sune") to solve it and
you can solve all the yellow face orientations that can occur.
The Sune leaves the corner by your left thumb unchanged (UFL);
it twists the other three corners Clockwise (CW) (it also cycles the UF, UR, and UB edge pieces).
The final U2 can often be skipped, if you do not need the original UFL corner to end up back at UFL.
R U R' U R U2 R' [U2] 

This is the Inverse Mu (or μ) pattern.
The wrong corners need a CCW twist, or two CW twists.
The final U2 can often be skipped.
Apply the Sune algorithm twice,
after placing the one correctly oriented corner at UFL before each Sune.

The AntiSune algorithm:
L' U' L U' L' U'2 L [U'2] The AntiSune leaves the corner by your right thumb unchanged (UFR); it twists the other three corners CounterClockwise (CCW). 

This is the Diagonal or Slash pattern.
Turn U', then apply Sune once, to get (rotated) Inverse Mu pattern, then solve that pattern. 
An easy alternative:
F' (r U R' U') (r' F R) This is the same as the CFOP OLL Double Square, preserving the bottom edge pieces. 

This is the Bug Eye pattern.
Apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that. 
The shorter Bug Eye algorithm:
(r U R' U') (r' F R) F'
Note the similarity to the previous algorithm (the F' moves from the beginning to the end of the algorithm). 

Pi pattern.
Apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that. 
This algorithm is easy to remember:
F (R U R' U') (R U R' U') F'. 

Headlight pattern.
First do U2, then apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube (U2) into the Inverse Mu pattern, and solve that. 
R' F' U' F U R
Or: U' F (R U R' U') F' Or CFOP: U2  R2 D R' U2 R D' R' U2 R' 

H pattern.
First do U to set up, then apply Sune algorithm once, to get the Mu pattern. Apply Sune algorithm again. 
F (R U R' U') (R U R' U') (R U R' U') F'  
Corners Oriented!
Done with this step. 
If you have correctly built the first two blocks, you will have all four bottom corners with "matching pairs", that is, the sides of the corner cubies will have the same color on a given face. Now find out if there are any matching pairs on the four top corners. Assuming you have not "flipped" a corner, either you will have 0, 1, or 4 matching pairs on the top corners. If you see more than one matching pair of corners on the top (yellow), then you have all 8 corner pairs matching and all corners are oriented  go to the LSE step. If you see one matching pair of corners on the top, then move that pair to B with Umoves. If you see no matching pairs of corners on the top, you either have 5 pairs (with one pair hidden on the Back), or you have 4 pairs and you'll have to do a second "5pair" algorithm with a U' in between them. (Warning: Do not use the "4 pair" algorithm from the Ortega Corners First method; it will mess up the FL and FR edges in your first two blocks.)
The "5pair" algorithm: R U' R F2 R' U R F2 R2.
Alternatively, with the one top pair on left, use the "Jperm" algorithm:
(R U R' U') R' F R2 U' R' U' R U R' F' or the related R U R' F' (R U R' U') R' F R2 U' R'.
If there are no top pairs (just the 4 pairs on the bottom), instead of two 5pair algorithms, use the "Yperm" algorithm:
F  R U' R' U'  R U R' F' (R U R' U') R' F R F'.
Both the Jperm and Yperm leave DF and DB unchanged.
The four top corners are now solved, though you might need to do a Ulayer move to line up the colors on the sides. Your cube should look like this:
Overview: First fix the centers by doing Mslice move(s). Fix orientation of the edges. Solve the UL and UR edges. Finally solve the four remaining edges in the M slice.
To fix edge orientation, you will use only Mslice and Uslice moves to get only white or yellow edge faces on the top and bottom. To solve the 2 UL and UR edges, use only Mslice and U2 moves. To solve the final 4 Mslice edges, use only Mslice and U2 moves.
Orientation refers to the presence of "good" and "bad" edges on the top and bottom. Do an Mslice move, if necessary, to get the yellow center on top of the cube. (Note that it does not matter how the Ulayer is turned; its edges need not match the bottom two layers.) Then count the number of nonwhite and nonyellow edges on the top and bottom of the cube — these are the "bad" edges. You will count 0, 2, 4, or 6 bad edges. (There cannot be 8 bad edges because you solved the Blue/White and Green/White edges at DL and DR when you built the first two blocks.)
If 0 bad edges (i.e., all the top and bottom edges are "good"), go to the next step.
If 4 bad edges, with 3 on top and 1 on bottom, you have the "arrow" pattern.
Turn the Ulayer so the middle of the arrow points the toward the "bad"
edge on the Dlayer.
Do either M or M'
to bring the bad edge on the bottom up to the middle of the arrow,
then U or U'
(it does not matter which way),
then M' or M
(opposite of the first move).
So if the bottom "bad" edge is at the front, point the "arrow" to the front,
then do M' U' M.
Or if the bottom "bad" edge is at the back, point the "arrow" to the back,
then do M U' M'.
If 4 bad edges, with 4 on top and 0 on bottom, you can easily make the "arrow" pattern
with M' U2 M, then follow the directions for "arrow".
(Remember the M' U2 M algorithm; it swaps the FU and FB edge pieces and often is used when solving the blue/yellow and green/yellow edges in the next step.)
In the pictures below, the pink edges denote "good" edges (white or yellow),
and purple shows "bad" edges (blue, green, red, or orange).
If 2 bad edges, with 1 on bottom at front, and 1 on top at back,
then do M' U' M  U' to get the arrow pattern.
If 2 bad edges, with 1 on bottom at back, and 1 on top at front,
then do M U' M'  U' to get the arrow pattern.
If 2 bad edges, with 2 on top at front and back,
then do M' U' M  U to get the arrow pattern.
If 2 bad edges, with 2 on top at right and back,
then do M' U' M  U2 to get the arrow pattern.
Your cube should have all Last 6 Edges with white or yellow up (or down, on the bottom layer).
Using Mslice and U2 moves (not U or U', which will mess up the edge orientation), get the Blue/Yellow and the Green/Yellow edges on the bottom front and bottom back positions. M' U2 M will swap the FD and FU edges. Likewise M U2 M' will swap the BD and BU edges.
When you have, say, the Blue/Yellow edge at FD, then turn the Ulayer so that the Green edged corners face you (think opposite colors on bottom and top). M2 will bring the Blue/Yellow edge between the two Blue corners then U' will line up the Ulayer.
Now you are down to Last 4 Edges. The H Pattern and the HX Pattern are easy to recognize and the algorithms are simple:
The 1223 Patterns are a little harder to set up. You are looking for the cubies around the Mslice where they match colors with a neighbor. There will be one cubie that does not match either neighbor in the Mslice, three cubies that match wrapping around a corner, and two other pairs that match. Rotate the Mslice so that the "1" cubie is in the Ulayer and the "3" cubies wrap around to the down layer. You will get a setup like one of those below, although your colors in the Mslice might not match those on the L and R.
Using the left diagram below, watch the Orange/White "1" cubie. Do U2 to move the Orange/White "1" cubie at FU to BU (away from the "3" cubies). Do M to move the Orange/White at BU to FU (toward where the "3" cubies were; this will also move the "3" cubies from FD to BD). Do another U2 to move the Orange/White cubie at FU to BU again. If you started with the same color setup as in the left diagram below, you finish with a M'. If you had a different color setup, rotate the Mslice whichever way you to to solve the cube.© 2020 Eric Krohn.
Simple Roux Method of Solving Rubik's Cube
by Eric Krohn
is licensed under a
Creative Commons AttributionShareAlike 4.0 International License.