Solving the PLL is the last step of the CFOP, and is the final straight in speedsolving the Rubik's cube. There are 21 different variations of Last Layer Permutations, and a well-known name for each. Therefore are required 21 algorithms to make a PLL solving in just 1 fast algorithm. It is possible to make 2 look PLL using only 6 algorithms, you can learn it in the speedsolving guide here. The algorithms are divided into groups based on their effect on the Rubik's cube (corners only, edge only, etc...). The PLL algorithms are very important to master and expertize in.
I had Bolded the algorithms that I use in my solving, which I find easiest for me. In some cases I included more than 1 algorithm, and they are all great algorithms. Just try them all and decide which one works best for you.
Some of the algorithms starts with (y) / (y') / (y2). I put it in round brackets because these are not actual moves (unlike such notations in a middle of an algorithm), because you have to 'y' rotate the cube anyway to get the required angle for any algorithm. It's just that these algorithms start with a different angle than the one shown in the image.

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The '[ ]' square brackets in the algorithms represents the fingertricks. The move sequences inside the [] are moves that can be done using fingertricks without breaks or re-grips in between, and with some practice they can become terribly fast. I kept the algorithms relatively empty of such notations, as there is no one approach for that, and everyone has his own style. Consider them as guidance only.

Pl 111-5

Edge Permutations Only

Algorithm Name	Image	Algorithm
Ua perm	[R U' R] U R U R U' R' U' R2 (y2) R2 U' R' U' R U R U R U' R
Ub perm	R2 U R U R' U' R' U' R' U R' (y2) R' U R' U' R' U' R' U R U R2
Z perm	M2 U M2 U M' U2 M2 U2 M' U2 (y) [U R' U'] R U' R U R U' R' U R U [R2 U' R' U]
H perm	M2 U M2 U2 M2 U M2

Corner Permutations Only

Pll Hun 1x11

Algorithm Name	Image	Algorithm
Aa perm	l' U R' D2 R U' R' D2 R2
Ab perm	l U' R D2 R' U R D2 R2
E perm	x' [R U' R' D] [R U R' D'] [R U R' D] [R U' R' D'] (y) x' [R U' R' D] [R U R' D'] [R U R' D] [R U' R' D']

Corner & Edge Swap Permutations

Algorithm Name	Image	Algorithm
T perm	[R U R' U'] R' F R2 U' R' U' [R U R' F']
F perm	[R' U R U'] R2 y' [R' U' R U] y x [R U R' U'] [R2 x U'] R' U2 R' d' R' F' R2 U' R' U R' F R U' F
Ja perm	[R' U L'] U2 [R U' R' U2] [L R U'] (y) L' U' L F L' U' L U L F' L2 U L U
Jb perm	[R U R' F'] [R U R' U' R' F] [R2 U' R' U']
Ra perm	[L U2' L' U2'] L F' L' U' L U L F L2' U (y) [R U R' F'] R U2 R' U2 R' F R U R U2 R' U'
Rb perm	[R' U2 R U2] R' F R U R' U' R' F' R2 U'
V perm	[R' U R' U'] [x2 y'] [R' U R' U'] [l R U'] [R' U R] U [R' U R' d'] R' F' R2 U' R' U R' F R F
Y perm	[F R U' R' U' R U R' F'] [R U R' U'] [R' F R F']
Na perm	{L U' R U2 L' U R'} {L U' R U2 L' U R'} U (y) {L U' R U2 L' U R'} {L U' R U2 L' U R'} U' (y) [R U' R' U] l U F U' R' F' R U' R U l' U R' (z) D R' U R2 D' R D U' R' U R2 D' R U' R
Nb perm	{R' U L' U2 R U' L} {R' U L' U2 R U' L} U' (y) {R' U L' U2 R U' L} {R' U L' U2 R U' L} U (z) U' R D' R2' U R' D U' R D' R2' U R' D R' (y) R' U R' F R F' R U' R' F' U F R U R' U' R

Pll 1x19

Pll 1x11

Corner & Edge Cycle Permutations (G perms)

Algorithm Name	Image	Algorithm
Ga perm	[R2 u] R' U R' U' R u' R2 y' [R' U R]
Gb perm	[L' U' L] y' {R2 u R' U R U' R u' R2} (y2) [R' U' R] y {R2 u R' U R U' R u' R2}
Gc perm	[R2 u'] R U' R U R' u R2 y [R U' R']
Gd perm	[R U R'] y' R2 u' R U' R' U R' u R2

Pl 111-275