Roux CMLL
There are 8 Roux letters (AH) and 6 roux swaps for each of the letters. This means that there can be at most 8x6=48 algorithms. However, if you do not count mirrors, inverses, and repeats, then there are only ~21 real cases.
Algorithm Notation: [Setup Moves] Main Algorithm
The setup moves are there to ensure easier recognition. Advanced users will be able to avoid the setup moves by recognizing the case from a different angle.
Breakdown Notation: <A: [B, C]> = A B C B' C' A'
In Group theory, A is known as a conjugate, and [B, C] is known as a commutator.
A  Oriented
There are 2 cases to memorize. A1 is just a skip.
A1  Double RowSkip 
All corners are correctly placed.  
A2  Bottom Row[U2] x (R' U R') D2 (R U' R') D2 R2 x'Breakdown: <R2: [(R U R'), D2]>

This is just an A perm. You can avoid the x rotations if you can regrip appropriately. I find the A perms easy to remember since they are just permutation commutators. Alternative: J(a): [U] (L' U R U' L) U2 (R' U R U2 R')
Alternative: J(b): [U'] (R U' L' U R') U2 (L U' L' U2 L)
Alternative J(b): [U] (R U R' F') (R U R' U') R' F R2 U' R'
Alternative T: (R U R' U') R' F R2 U' R' U' (R U R' F')
Alternative: J(a): (R' U L') (U2 R U') (R' U2 R2) x'
Alternative: R2 F2 R U L' U2 R U' L


A6  Diagonal swapR2 U' R F' R' U r2 U (F U F') 
Perform this as (R2 U' x' R D' x R' U r2 U y' R U R' y), but keep the transition between rotations short. Alternative N(b): (R' U L' U2 R U' L)2
Alternative Y: F R U' R' U' (R U R' F') (R U R' U') (R' F R F')
Alternative E: x' R U' R' D R U R' D' R U R' D R U' R' D' x

B  Antisune
There are 6 cases to memorize. Every sune case is a mirror of the antisune case, so learning these 6 cases will help you learn another 6. So try to understand how the algorithm works; you will need to mirror it later. Also, all antisune algorithms are left handed algorithms. This makes them easy to remember.
B1  Right Column[U'] L' U' L U' L' U2 LMirror: C1
Breakdown: [L', U'] [U2, L']

Alternative: [U] R' U' R U' R' U2 R
Alternative: [U2] R U2 R' U' R U' R'


B2  Double Column[U] (L2 D L' U L D' L' U L') U' L U' L'Mirror: C2
Breakdown: <L: [(L D L'), U)]> [L, U2] [U, L]

This is a variation of a D swap. Alternative: [U'] R' F U2 F' R F R' U2 R F'
Alternative: [U']R2 D R' U R D' R' U R' U' R U' R'


B3  Backslash[U'] (F' L F L') U2 (L' U2 L)Mirror: C3
Breakdown: [F', L] [U2, L']

This is just inverse sledgehammer, with alternate slotting. Alternative: [U2] (R' F R F') U2 F' U2 F
Alternative: x' F U' R U L' U2 R' U2 R


B4  X CaseF U2 F' U2 (F' L F L')Mirror: C4
Breakdown: [F, U2] [F', L]

This is just taking a F2L pair out, and inserting using sledgehammer. Alternative: [U'] R U2 R' U2 (R' F R F')


B5  Forward Slash[U'] L' U R U' L U R'Mirror: C5
Breakdown: [L', (U R U')]

This is the AntiNiklas 

B6  Left Column[U] L' U' L U' (L F' L' F) L' U2 LMirror: C6
Breakdown: <U2: [L', U']> [L, F'] [L', U2]

Mirror of C6. Ignoring the brackets (sledgehammer), this is the antisune. Alternative: [U] R U2 R' U' R U' (B U B' U') R'
Alternative: U' R' U' R U' L U' R' U L' U2 R

C  Sune
There are 0 cases to memorize. Assuming you've learned the antisune algorithms, you should be able to learn sune instantly. Remember that right handed algorithms are sune algorithms.
C1  Left Column[U] R U R' U R U2 R'Mirror: B1
Breakdown: [R, U][U2, R]

This is the mirror of B1. Alternative: [U'] L U L' U L U2 L'


C2  Double Column[U'] (R2 D' R U' R' D R U' R) U R' U RMirror: B2
Breakdown: <R': [(R' D' R), U')]> [R', U2] [U', R']

Mirror of B2. 

C3  Forward Slash[U] (F R' F' R) U2 (R U2 R')Mirror: B3
Breakdown: [F, R'][U2, R]

Mirror of B3. Alternative: [U2] (L F' L' F) U2 F U2 F'


C4  X CaseF' U2 F U2 (F R' F' R)Mirror: B4
Breakdown: [F', U2] [F, R']

Mirror of B4. Alternative: [U] L' U2 L U2 (L F' L' F)


C5  Backward Slash[U] R U' L' U R' U' LMirror: B5
Breakdown: [R, (U' L' U)]

Mirror of B5. This is the Niklas. 

C6  Right Column[U'] R U R' U (R' F R F') R U2 R'Mirror: B6
Breakdown: <U2: [R, U]> [R', F] [R, U2]

Mirror of B6. Ignoring the brackets(sledgehammer), this is the sune. Alternative: [U'] L' U2 L U L' U (B' U' B U) L

D  Bowtie / L
There are 3 cases to memorize. D1 is a repeat of C1, D2 and D3 are mirrors, and D4 and D5 are mirrors.
D1  Backslash + Opposite PairedR U2 R' U' (R U R' U')2 R U' R'Repeat: (C1)3
Breakdown: ([R, U][U2, R])3

This is just a triple antisune. You could also perform a triple sune. Alternative: [U2] (R' D R' D R') U (R' D R' D R')'
Alternative: R U R' (U R U' R')2 U R U2 R'


D2  Front Paired + Forward Slash[U] R' U2 R' D' R U2 R' D R2Inverse: E5
Mirror: D3

This is the inverse of E5. The way I remember it is, the front needs to be broken. By doing U move, you change the situation to a backslash + front broken. Then execute the inverse of the Headlights case back slash. 

D3  Forward Slash + Front BrokenL U2 L D L' U2 L D' L2Inverse: E3
Mirror: D2
<(L U2): [(L D L'), U2]>

This is the inverse of E3. Easy to remember since this is the inverse of the Headlights case forward slash. Alternative: U2 R' U' R U2 L' U R' U' L U' R


D4  Top Paired + Front Paired[U2] (F R' F' R) U (R U' R')Inverse: F5
Mirror: D5
Breakdown: [F, R'] [U, R]

You will notice a Right Column on performing [U2]. This toppaired pattern indicates you can use the inverse sledgehammer followed by alternate slotting. Alternative: L' U' L' U R U' L U x'


D5  Top Paired + Front Broken[U'] (F' L F L') U' (L' U L)Inverse: F3
Mirror: D4
Breakdown: [F', L] [U', L']

You will notice a Left Column on performing [U']. This toppaired pattern indicates you can use the inverse sledgehammer followed by alternate slotting. Alternative: x L' D L U' L' D' L U x'


D6  X PairedL' U2 R U' R' U2 L R U' R'Breakdown: [(L' U2 R), U'] [(U R), U']

Alternative: [U] R U R' U R U2 (B U B' U') R'
Alternative: [U'] R U R2 F2 r F R' F2 R
Alternative: L' U2 R U' Rw' U2 R Lw U' R'

E  Headlights / U
There are 4 cases to memorize. E3 and E5 are not only mirrors, but they're just inverses of D cases, so you should already be knowing them.
E1  Bottom Row(R' U' R U' R' U2 R) (R U R' U R U2 R')Inverse: F1
Breakdown: [R', U'] [U2, R'] [R, U] [U2, R]

This is just the antisune followed by a sune. This is the inverse of F1. 

E2  Double Row[U] B L2 D L' U L D' L2' U' B'Breakdown: <B: [(L2 D L'), U]>

This is similar to other Dswaps. 

E3  Forward SlashL2 D L' U2 L D' L' U2 L'Inverse: D3
Mirror: E5
Breakdown: <(U2 L): [(L D L'), U2]>

This is very intuitive and easy to execute. Perform all D moves with your right hand, and all L moves with your left hand. The U moves can be done with any hand. 

E4  X Case[U2] R' F U' R F R' U R F'Inverse: F4

Track the F2L pairs in the Front Left and Back Right. 

E5  Back SlashR2 D' R U2 R' D R U2 RInverse: D2
Mirror: E3
Breakdown: [(R2 D' R), U2] [U2, R']

Very easy; just mirror E3. Hands switch. You may use the same hand for U moves if you prefer. 

E6  Top Row[U'] F R U R' U' F'Breakdown: <F: [R, U]>

You probably already know this. 
F  Chameleon / T
There are 2 cases to memorize. F1 and F4 are just inverses, and F3 and F5 are both mirrors and inverses.
F1  Double Row(R U2 R' U' R U' R') (R' U2' R U R' U R)Inverse: E1
Breakdown: [R, U2] [U, R] [R', U2] [U', R']

This is just an antisune followed by a sune. This is the inverse of E1. 

F2  Bottom RowR' U Rw U2 R2' F R F' R 
This takes out an F2L pair from the back, moves it to the left side, then inserts it from the front, while fixing the left block.  
F3  Right Column[U] (L' U' L U) (L F' L' F)Inverse: D5
Mirror: F5
Breakdown: [L', U'] [L, F']

This is just the mirror of F5 Alternative: U' R' U' R U L U' R' U x


F4  Top RowF R' U' R F' R' U F' RInverse: E4

Track the F2L pairs in the Front Left and Back Right. Alternative: F U' L' U R2 U' L U R' Lw' U' x'


F5  Left Column[U'] (R U R' U') (R' F R F')Inverse: D4
Mirror: F3
Breakdown: [R, U] [R', F]

This is just the mirror of F3. 

F6  Double Column[U2] R U' (R2 D' r U2 r' D R2 U R')Breakdown: [(R U' R2 D' r), U2]

This is essentially a D swap. Alternative: R' U R2 D Rw' U2 Rw D' R2' U' R
Alternative: [U2] L' U (L2 D l' U2 l D' L2 U' L)

G  Pi
There are 4 cases to memorize. G1 is just a repeat of E6, and G4 is an inverse of G2. Technically, G3 and G6 are the only new algorithms, and the others are just a combination of older algorithms.
G1  Right ColumnF (R U R' U') (R U R' U') F'Repeat: (E6)2
Breakdown: (<F: [R, U]>)2

This is just (E6)2. Alternative: R U2 R2' U' R2 U' R2' U2 R


G2  Back Slash(R' U' R U' R' U2 R) U' (L' U R U' L U R')Inverse: G4
[R', U'] [U2, R'] <U': [L', (U R U')]>

This is the antisune followed by the Antiniklas. 

G3  X Casel' U2 (y) R U2 R' U2 R' U2 (y) rInverse: H4

Notice the similarity with H4.
Alternative: L' U2 y R U2 R' U2 R' U2 F y x


G4  Forward Slash(R U R' U R U2 R') U' (R U' L' U R' U' L)Inverse: G2
Breakdown: [R, U] [U2, R] <U': [R, (U' L' U)]>

This is the Sune followed by Niklas. 

G5  Double ColumnR U' L' U R' U L U L' U LInverse: H3
Breakdown: [R, (U' L' U)] U' [L', U2] [U', L']

This is the shorter version of (Niklas)(Sune). The longer version is (R U' L' U R' U' L) (L' U2 L U L' U L). Alternative: R' U L U' R U' L' U' L U' L'


G6  Left Column(L' U' L U' L' U) L F R U R' F' 
This is begins with antisune, but uses alternate slotting in the end. It's a shorter form of (L' U' L U' L' U2 L) L' U' L (F R U R' F'). Alternative: [U2] R U R' U R U' y R U' R' y L'

H  Double Headlights / H
There are 0 cases to memorize. H1 is a repeat of C1, H3 is an inverse of G5, H4 is an inverse of G3, and H6 is a repeat of E6.
H1  Double Column[U] R U R' U R U' R' U R U2 R'Repeat: (C1)2
Breakdown: ([R, U][U2, R])2

This is a double sune. You can also perform a double antisune. Alternative: R U2 R' U' R U R' U' R U' R'


H3  Bottom Row[U] L' U' L U' L' U' (R) U' L (U L')Inverse: G5

Ignoring what's in brackets, this is an antisune. This is basically doing (Antisune)(Niklas). Alternative: [U'] R U R' U R U (L') U R' (U' L)


H4  Right Column[U2] r' (y') U2 R U2 R U2 R' (y') U2 lInverse: G3

It's faster to recognize this as left column and skip the setup move. Alternative: (F R U R' U' F') (R U R' U' R' F R F')
Alternative: l' U2 (y) R U2 R U2 R' U2 (y) r


H6  Double RowF (R U R' U')3 F'Repeat: (E6)3
Breakdown: (<F: [R, U]>)3

This is just (E6)3. 