One corner and two adjoining edges are correct

The usual notation U, R, D, L, B, F is extended to slice and antislice moves.
Us,Rs,Ds,Ls,Bs,Fs are slice moves UD',RL',DU',LR',BF',FB'.
Ua,Ra,Da,La,Ba,Fa are antislice moves UD,RL,DU,LR,BF,FB.
Sr, Sl, Sf, Sb, Su, Sd are the center slice moves adjoining faces R,L,F,B, U,D.
[P*Q] means the same as P Q P'
[P;Q] means the same as P Q P'Q'
Lowercase letters u,r,d,l,b,f represent twists of the whole Cube, so that u = UsSu, r = RsSr and so on. For example dFR'U = LF'Ud = LF'U.
Character ^ represents mirroring (usually R<->L).

The numbers in the second column denote the number of quarter moves and face moves.

This is a set of algorithms for solving positions in the last layer when one corner and two adjoining edges are correct.

Some of these positions are already included in sections dealing with corners and edges and in the section on twisting and flipping cubes in place. They are again included here for the completeness.

U²R²U'L'U R²U'L U' 12,9
R'D R'U²R D'R'U²R² 12,9
U²B'U'B U'L²D F'D'L² 13,10
L F'R F²L'F L F²R'aF 13,11
R'U'R'U R U²B U B'U F R F'R 15,14
R B'R'U'B'U F U'B U R B R'F' 14
U'F²U L²D'L U L²D L²U'L F² 18,13
R'F²R D'R'D F²D'R D 12,10
L²D²L U²L'D²L U²L 14,9
R²B'R F²R'B R F²R 12,9
L'B D²R'D R D B'L'D F D'L² 15,13
L'F L F'D R'D R D²L D'L'D F 15,14
L²D F'D'F'D F L F L'D'L F'L 15,14
L²B R'D²R B'L'F²L'F' 13,10
R'F²R F²D F'R'F R F D' 13,11
R'F L'F R F'L F²R'F R F 13,12
R'D'F'D F'R U L D F²D'L'U'F' 15,14
U B'U'L'B'L F'L'B L U B U'F 14
R'D R²U'R²D'R'U R²D'F²D F²
L U L'F²L U'L'U F²U' 12,10
D R²D L²D'R²D L²D² 14,9
U L D'L'U'L D L' 8
R'D'R U'R'D R U 8
L F'R F R'aF²R F R'F² 13,11
U'R²UsF'D F L'U'R²U L F' 15,12
U'R²D'R²U L F'D'F'D F L'D 15,13
U'R U F D'F D R D'R'F'R D F'R' 15
U²F'U F U²L²D F'D'L²B'U B 17,13
U'R²B D'F²U'F U F'U F²D B'U 17,14
D'F U F'D F L D L'U'L D'L'F' 14
D L'B²L D'F²D L'B²L D'F² 16,12
[L'B L U B U';F²] 16,14
R'F²R'B'R F²R'B R² 12,9
L D R²D'L'F U F'DsR²D'F' 15,13
L²B R'D²RsF'L B'L'F'L'F' 15,13
U'F D F D'F L²B'U B L²F U 15,13
U'R'D'R U R'D R 8
L D'L'U L D L'U' 8
L'F²L'B'R U²R'B L²F' 13,10
L'F U F U'F'L F²U F²U' 13,11
L F L'F²R F'L F R'F L'F 13,12
R'D'F'D F D²L D L'D R F 13,12
U L D'L²B'L'B L'D L'U'F' 13,12
R F'L'FaU²B'R²F²L F'R F' 16,13
L D'F²D L'D'L F²L'D 12,10
R F'L'F R'F'L F 8
L'F L'F'D F²L F²L'D'F L² 15,12
D²F L'D'F²D F²L F'D'F D' 15,12
U'F²U²F U²F U L'F U F U'F'L 17,14
U'aF²U²F U'F'U'F²D R U R' 16,13
U F U²B'R'F'R FaU²F²U'F 16,13
R'D'L'U'F'U F'L D R U F U'F 14
U²F'U'L'U'L²F'L²U'L U F² 16,12
U²F'U'R'U L'U'L U'F'U F R U'F 16,15
U L U L'U B²D'R D B²U 13,11
D²B R²U'R U R B'U'B R B'U D² 17,14
U'F'U²L'U'L²F'L'F² 12,9
R U'R'U F'L U L'F L U'L' 12
R'D F D'R D F'D'R U'R'U 12
R'F D²B'D F D'B D²F'R F' 14,12
R F'U²B U'F U B'U²F R'F' 14,12
R B'R²F R F'R²B R'U'R'U 14,12
R B'R²F D'F D F'R²B R'F' 14,12
R'B R²F'U F U'F R²B'R F' 14,12
L U'F²U²F L F'L'U²F U F L' 16,13
L F R'F²R²F U F'U'R²F Rs 16,13
U R'U²F D'F'U F²D F'U R U'F' 16,14
U R'D²L'D L D'L D²R U'F² 15,12
L'D R²U R'U R U'R²D'L F² 15,12
R B²D F'L²F D'B'U²B'U'R' 15,12
U F L'U L U²R'D'F'L D'L'D²R 16,14
R F U²F²U'aF U F'D F²U²R'F' 18,14
R'F L'D'L F L'D L F'R F' 12
R'F D'L F L'D L F'RsF' 12
R'F'U F²D'F D F²U'F R F' 14,12
R'F²L F'R F L'F²R U'R'U 14,12
R'F²L F'D'F D F L'F²R F' 14,12
L'U²R B'R B R'U²L U'R'U 14,12
L'U²R U R'U²L U'F'U'F U 14,12
L F²L'F'U'F'U F L F²L'F' 14,12
L'F'L F R F'U L'F L U'F R'F' 14
L'F'L UaF U'R F R'UsF'U' 14
U²B U²R U'R'B'R U R F R²F' 16,13
L D R F U F'U'F'R'F²D'F²L'F' 16,14
R²F R F'R'F²D'F'D F'U'R'U R² 17,14
R F U F'R'U F L F'U'R U L'U²R'F' 17,16
R B'U R U R'U'B U²R U²R² 15,12
R'F²R F'U'B'D R'D'B U F' 13,12
R U'R'F²U²B U'F U F'aU²F²U 18,14
U F'L D'F'D L'F U'F'D'F D F 14
U F DsR F'R'U F'U'aL'F L 14
U²F'U'L'U'B U L U'L²B'L²F 16,13
D F²R F²U F L F L'F'U'R'D'F 16,14
U R U'B'D'F R'F'D B R²F R F' 15,14
R F²D F D'F L²B'U B L²R' 15,12
D R²U'aR U R'D R²U'R Us 15,13
D R B'R U'R U R²B R'U'R Us 15,14
U'F²U²FaU'F'U B'U²F²R U R' 18,14
D R F'U F DsF D'R'D F'D² 14,13
R F'L'U'F'U B D L'D'FsL U R'F 16
L²F R'F'D²F²D F'D'F'D²L²R 18,13
U²R²U R²B R'U'R U R B'U 15,12
U'R²U R'U'R²UaR'U'R Us 15,13
DsR U F R F'aR F R'B R'F'D' 15
R'D²L D L'F D R U²L'U'L F'U' 16,14
U L²F²R'F L'F'RaF²L²F'U'F 18,14
R F'L U L'F L U'L'F R'F' 12
RsF'L U L'F L U'F R'F' 12
D'R D F'U F U'F D'R'D F' 12
R F D'F²U F U'F²D F'R'F' 14,12
D²F D'R D F'UsF'U'F R'D' 14,13
R²F R F'U'F'aR B R'F R²U 15,13
R F R²B U F'R'F U'B'D'R D F' 15,14
U'aR D'R'B R²D R²D'B'R U D² 17,14