Algorithms are the series of moves done to help solve a cube or for making cool patterns. I will be updating this with the algorithms I use in my videos.
I personally like visuals so I have embedded the videos in this page as well is the algorithms are a bit confusing to understand. The algorithms are meant to accompany the video so they might be a bit confusing without. 

Full OLL and PLL Algorithm list

How to solve a Rubik's Cube (Beginner Method)
Corner twisting algorithm  R' D' R D
Edge insertion algorithm (U R U' R') (U' F' U F) or (U' L' U L) (U F U' F') depending if you need to insert it on the right slot or left after lining up edge with center color. Making the top cross: If you have a horizontal bar  F (R U R' U') F' If you have a J shape in the top left  F (R U R' U')2x F' If you only have the center dot just do either one of these. Solve corners on PLL stage (Put headlight in back)  (R' F R' B2) (R F' R' B2) R2 If you don't have any headlights do this once and then you will. Solve Edges on PLL stage  (R U' (R U R U) R U') R' U' R2 If only three edges need to be solved put solved bar in back and do alg. 1 or 2 times 

4x4 Edge Method
Edge Pairing (slice  flip  slice back)  Uu'  R U R' (F R' F' R)  Uu
4x4 Beginner Method
OLL parity algorithm (Also used to swap edges on any large cube like 5x5):
r' U2 l F2 l' F2 (r2 U2 r U2 r' U2) F2 r2 F2 Faster OLL Alg (All R moves are going to be two layers (Usually noted Rr or 2R) but will be represented as just R for simplicity sake of the text.) R’ (U2 R U2 R U2) R2 F2 (R’ U2 R’ U2) F2 R2 F2 PLL Parity algorithm  r2 U2 r2 Uu2 r2 u2 

Supercube algorithms
(This includes shape modes like the Fisher Cube, Mastermorphix, etc.) Turn the top center 180°  (R U R' U)5x
Turn the front and left side center 90°  (M' U M) E (M' U' M) E' 

Supercube algorithms 4x4 and larger
(This includes shape modes like the Fisher Cube, Mastermorphix, etc.) Cycles FDR (Front face  down/right piece) to UDR (Up face  Down/Right) to FDL
r U l' U' r' U l U'  Switch the top and left three center pieces on the U face. (r' u r U) (r' u' r U) (r' u r U2) r' u' r "Safe" OLL parity algorithm that wont mess up the center (lowercase indicates an inner slice and not turning two faces) r' U2 l F2 l' F2 (r2 U2 r U2 r' U2) F2 r2 F2 "Safe" PLL parity algorithm that wont mess up the center (lowercase indicates an inner slice and not turning two faces) r' (U' R U F R2 F') r l (F R2 F' U' R' U) l’ 

2x2 Beginner Method
Corner twisting algorithm  R' D' R D
Aperm one set of headlights in back  (R' F R' B2) (R F' R' B2) R2 

2x2 Ortega Method
Headlights on one side on left  F (R U R' U') F'
Headlights on one side on left and other corners pointing out  F (R U R' U')2x F' Headlights on both sides  F (R U R' U')3x F' or R2 U2 R U2 R2 Sune on right  R U R' U R U2 R' Sune on left  L' U' L U' L' U2 L "Hammerhead" shape on left  (R U R' U') (R' F R F') Two opposite corners  (R' F R B') (R' F' R B) Aperm one set of headlights in back  (R' F R' B2) (R F' R' B2) R2 Tperm one set of headlights on left  (R U R' U') R' F R2 (U' R' U' R) U R' F' Yperm  F (R U' R' U') R U R' F' (R U R' U') (R' F R F') PBL (permute both layers) Dual Headlights on back  (R2 U' R2) y U2 (R2 U' R2) Single headlights on front on top  (R U' R) F2 (R' U R') Single headlights on front on bottom  (R' D R') F2 (R D' R) No headlights  R2 F2 R2 

Cuboid Algorithms (2x3x3)
Swap front/right corner on top and bottom layer  R2 U R2 U' R2
Swap corners on the back in the U layer  R2 F2 (U F2 U') R2 (U F2 U') R2 Swap D/F edge with U/B  B2 (D2 R2)3x B2 Swap U/F and U/B edges  (R2 U2)3x Swap U/F and U/R Edges  (R2 U)2x (R2 U2)2x (R2 U) (R2 U')2x 

Void Cube Parity
Adjacent edges on U/B and U/R:
(M' U)2x (M' U')2x M' U2 (M' U')2x 