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No explanation, just a new notation and the minimal alg list needed to learn square-1.

Notation:
R = Move the right half of the puzzle 180 degrees (clockwise)
u = move the U slice clockwise one “notch” Could be either (1,0) or (2,0) by old notation depending on what piece is to the right of the U notch.
u2 = move the U slice clockwise 2 “notches” Only used if there are 2 edges to he right of the U notch.
U = move the U slice clockwise 90 degrees. (3,0) in old notation
u4 = (4,0) in old notation
u5 = (5,0) in old notation
U2 = 180 degrees, (6,0)

Method:
Cubeshape: R u d’ R’ U’ d4′ R u2′ D R u’ d’ R U’ R
M2: u R u’ d’ R’
single EO: d’ R U’ R’ u4 d R u4′ d’ R’ U R
J/J: R U’ R’ U D R D’ R’
N/J: R U R’ U’ R U R’ U’ R
Adj/adj: d R U’ R’ u d R u d’ R’
Opp/opp: u R u’ d’ R’ U2 R u d R’
Pure parity: R U’ R’ D R D’ R’ D R u R’ d R u’ R’ u4 R d2′ R’ d2 R u4′ d R U R’
Flip E Slice: R U2′ R U2′ R