rokirovka: I personally prefer the following coordinate system over the A-T, 1-19 system and the Audouard coordinate system.
The problem with the existing algebraic notation for go is that while the letters and numbers A, B, C, D, E, F, G, H, J, K and 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are natural to identify with points on the board in one's mind, the letters T, S, R, Q, P, O, N, M, L and numbers 19, 18, 17, 16, 15, 14, 13, 12, 11 are much less natural, especially since one is counting and alphabetizing backwards as the points go away from the corner and sides, the opposite of the A, B, C . . . and 1, 2 , 3 . . . points.
The double-number and double-letter notations, such as Audouard coordinates, are also hard for me to keep clear in my head when there are more than two or three moves. For example, if I memorize a joseki as Black 3-4, White 5-3, Black 7-3, White 5-5, Black 4-6, White 8-4, the numbers are already blurring together indistinctly in my head. For me, the Audouard coordinates are no better: Black a34, White a53, Black a73, White a55, Black a46, White a84 is just as much a blur in my head. It's much easier to memorize Black C4, White E3, Black G3, White E5, Black D6, White H4. That I can visualize in my head. The problem is that Black R16, White P17, Black N17, White P15, Black Q14, White M16 is a blur again with the bigger numbers and letters in the middle of the alphabet and everything going backwards.
Thus, I personally find it much easier to follow an algebraic notation where all four corners are marked as A, B, C, D, E, F, G, H, J and 1, 2, 3, 4, 5, 6, 7, 8, 9 and asterisks are used to mark the right side and the top side. K and 10 of course never need asterisks. Thus I can notate the above joseki in the top right corner as Black C*4*, White E*3*, Black G*3*, White E*5*, Black D*6*, White H*4*. I say the moves in my head as "Black C-star-4-star, White E-star-3-star," etc. As an added bonus, I can instantly recognize a tenuki in a different part of the board because the asterisks are different. If I am analyzing a position in only one corner of the board, I can leave out the "stars" as I note the moves in my head as I calculate.
Here is an example of my notation recording the beginning moves of a game I like, Cho Chikun vs. Kato Masao, 7th Kisei, Challenger Final, Game 2, 16 December 1982. See how far you can follow the opening moves in your head as you read them.
1. C*4* D4* 2. D*3 C3 3. E*3* C*5 4. C*7 E*5 5. F*4 D*8 6. C*4 B*4 7. D*7 F*5 8. G*4 E*7 9. E*8 C*8 10. F*7 E*6 11. E*9 C*10 12. B*3 D*10 13. B*5 C*6 14. C6* tenuki! F4* 15. B4* C3* 16. C9* J*3* 17. F4 C6 18. H*6 H3 19. K3 E*4 20. E*3 K4 21. J*3 G5 22. D4 C4 23. D6 C7 24. G4 H4 25. H5 G6 26. J5 G2 27. D3 E2 28. D7 D8 29. E8 D2 30. E9 F7 31. C8 B8 32. C9 C*6* 33. D5
Here is a diagram showing the name of each point on the 19x19 goban in this coordinate system:
A1* B1* C1* D1* E1* F1* G1* H1* J1* K1* J*1* H*1* G*1* F*1* E*1* D*1* C*1* B*1* A*1*
A2* B2* C2* D2* E2* F2* G2* H2* J2* K2* J*2* H*2* G*2* F*2* E*2* D*2* C*2* B*2* A*2*
A3* B3* C3* D3* E3* F3* G3* H3* J3* K3* J*3* H*3* G*3* F*3* E*3* D*3* C*3* B*3* A*3*
A4* B4* C4* D4* E4* F4* G4* H4* J4* K4* J*4* H*4* G*4* F*4* E*4* D*4* C*4* B*4* A*4*
A5* B5* C5* D5* E5* F5* G5* H5* J5* K5* J*5* H*5* G*5* F*5* E*5* D*5* C*5* B*5* A*5*
A6* B6* C6* D6* E6* F6* G6* H6* J6* K6* J*6* H*6* G*6* F*6* E*6* D*6* C*6* B*6* A*6*
A7* B7* C7* D7* E7* F7* G7* H7* J7* K7* J*7* H*7* G*7* F*7* E*7* D*7* C*7* B*7* A*7*
A8* B8* C8* D8* E8* F8* G8* H8* J8* K8* J*8* H*8* G*8* F*8* E*8* D*8* C*8* B*8* A*8*
A9* B9* C9* D9* E9* F9* G9* H9* J9* K9* J*9* H*9* G*9* F*9* E*9* D*9* C*9* B*9* A*9*
A10 B10 C10 D10 E10 F10 G10 H10 J10 K10 J*10 H*10 G*10 F*10 E*10 D*10 C*10 B*10 A*10
A9 B9 C9 D9 E9 F9 G9 H9 J9 K9 J*9 H*9 G*9 F*9 E*9 D*9 C*9 B*9 A*9
A8 B8 C8 D8 E8 F8 G8 H8 J8 K8 J*8 H*8 G*8 F*8 E*8 D*8 C*8 B*8 A*8
A7 B7 C7 D7 E7 F7 G7 H7 J7 K7 J*7 H*7 G*7 F*7 E*7 D*7 C*7 B*7 A*7
A6 B6 C6 D6 E6 F6 G6 H6 J6 K6 J*6 H*6 G*6 F*6 E*6 D*6 C*6 B*6 A*6
A5 B5 C5 D5 E5 F5 G5 H5 J5 K5 J*5 H*5 G*5 F*5 E*5 D*5 C*5 B*5 A*5
A4 B4 C4 D4 E4 F4 G4 H4 J4 K4 J*4 H*4 G*4 F*4 E*4 D*4 C*4 B*4 A*4
A3 B3 C3 D3 E3 F3 G3 H3 J3 K3 J*3 H*3 G*3 F*3 E*3 D*3 C*3 B*3 A*3
A2 B2 C2 D2 E2 F2 G2 H2 J2 K2 J*2 H*2 G*2 F*2 E*2 D*2 C*2 B*2 A*2
A1 B1 C1 D1 E1 F1 G1 H1 J1 K1 J*1 H*1 G*1 F*1 E*1 D*1 C*1 B*1 A*1
DPledger: I have a minor suggestion for rokirovka's system. Instead of using the asterisk ( * ), try using the prime mark ( ′ ). It is already used frequently in mathematics for coordinate transformations, so this would be a natural application of the symbol. It is also typically pronounced, so A′3 would be spoken as "A prime 3".
bugcat: My practical problem with this is that (unless you're using a font where each character has the same spacing) the prime mark is not very visible.
Robert Pauli: I'd prefer the prime if I had to write down the moves myself, that's for sure. By the way, if you apply the modifier, it disappears completely.
Version with each tile having the same width:
A1* B1* C1* D1* E1* F1* G1* H1* J1* K1* J*1* H*1* G*1* F*1* E*1* D*1* C*1* B*1* A*1*
A2* B2* C2* D2* E2* F2* G2* H2* J2* K2* J*2* H*2* G*2* F*2* E*2* D*2* C*2* B*2* A*2*
A3* B3* C3* D3* E3* F3* G3* H3* J3* K3* J*3* H*3* G*3* F*3* E*3* D*3* C*3* B*3* A*3*
A4* B4* C4* D4* E4* F4* G4* H4* J4* K4* J*4* H*4* G*4* F*4* E*4* D*4* C*4* B*4* A*4*
A5* B5* C5* D5* E5* F5* G5* H5* J5* K5* J*5* H*5* G*5* F*5* E*5* D*5* C*5* B*5* A*5*
A6* B6* C6* D6* E6* F6* G6* H6* J6* K6* J*6* H*6* G*6* F*6* E*6* D*6* C*6* B*6* A*6*
A7* B7* C7* D7* E7* F7* G7* H7* J7* K7* J*7* H*7* G*7* F*7* E*7* D*7* C*7* B*7* A*7*
A8* B8* C8* D8* E8* F8* G8* H8* J8* K8* J*8* H*8* G*8* F*8* E*8* D*8* C*8* B*8* A*8*
A9* B9* C9* D9* E9* F9* G9* H9* J9* K9* J*9* H*9* G*9* F*9* E*9* D*9* C*9* B*9* A*9*
A10 B10 C10 D10 E10 F10 G10 H10 J10 K10 J*10 H*10 G*10 F*10 E*10 D*10 C*10 B*10 A*10
A9 B9 C9 D9 E9 F9 G9 H9 J9 K9 J*9 H*9 G*9 F*9 E*9 D*9 C*9 B*9 A*9
A8 B8 C8 D8 E8 F8 G8 H8 J8 K8 J*8 H*8 G*8 F*8 E*8 D*8 C*8 B*8 A*8
A7 B7 C7 D7 E7 F7 G7 H7 J7 K7 J*7 H*7 G*7 F*7 E*7 D*7 C*7 B*7 A*7
A6 B6 C6 D6 E6 F6 G6 H6 J6 K6 J*6 H*6 G*6 F*6 E*6 D*6 C*6 B*6 A*6
A5 B5 C5 D5 E5 F5 G5 H5 J5 K5 J*5 H*5 G*5 F*5 E*5 D*5 C*5 B*5 A*5
A4 B4 C4 D4 E4 F4 G4 H4 J4 K4 J*4 H*4 G*4 F*4 E*4 D*4 C*4 B*4 A*4
A3 B3 C3 D3 E3 F3 G3 H3 J3 K3 J*3 H*3 G*3 F*3 E*3 D*3 C*3 B*3 A*3
A2 B2 C2 D2 E2 F2 G2 H2 J2 K2 J*2 H*2 G*2 F*2 E*2 D*2 C*2 B*2 A*2
A1 B1 C1 D1 E1 F1 G1 H1 J1 K1 J*1 H*1 G*1 F*1 E*1 D*1 C*1 B*1 A*1