Edges, corners, triangles: 6 algorithms. Full course with animations and simulator: strefa-kostek.pl/en/kursy
Hold the FTO vertex towards you: U top, R right, F bottom, L left; at the back B (opposite F), BR (opposite L), BL (opposite R), D (opposite U). Letter = a face turned 1/3 of a turn clockwise, looking at that face; ' = the other way.
Whole-puzzle rotations: T = quarter turn around the front vertex (U to where R was), Uv = around face U, x2 = flip over (U to where D was). Opposite colours: white-yellow, green-blue, red-orange, purple-grey. Triangles do not matter until stage 6.
3 edges on the white face U; looking from above, clockwise: blue, red, purple.
Slot on the right (Uv). Faces F, BR, BL, D are free - use them to bring the edge onto face R:
On F: turn F until it is on R-F. At the back: BR / BL / D onto F or BR. On top in the wrong place: turn the face under it (L, B).
x2 - white at the back bottom. The edge's bottom face at the front (Uv), edge on the top side U-B (turn U):
Top face colour = fourth colour of the corner with white and the colours of the two bottom faces next to it. Wrong edge in a slot: insert any edge into it - it pops out. Last 3: turn U.
The corner's 4 colours = the colours of the faces around its vertex (twist does not matter).
Front and back: correct corner at the back; the corner belonging at the front to the top right corner (T), U F U' F'; repeat (at most 2x).
Square: one correct - to the top left (T), F U F U' F, once more if needed. None - once and start over.
Twisted one at the front, the other to the top right (T). Two opposite (front-back): the algorithm with a correct one in the top right, then once more.
Groups: white, green, grey, orange | red, purple, blue, yellow. Two faces of a group touch at a single vertex.
R F' L F L' R U L' U' L R = triangle from the right corner of F to the right corner of U (from the right of U to the left of F, from the left of F to the right of F).
Shared vertex at the front, face being solved on top, face with the triangle you need at the bottom. U: wrong triangle to the right corner of U, F: the needed one to the right corner of F, algorithm, undo F, undo U. The last face of a group solves itself.