The Old Chess Books still available as ebooks especially by Mason, Ed Lasker and old Soviet books were very good at teaching chess. Reinfeld revised the Mason series, and probably a lot more.
All great players learned the laws of Opposition.
Below are the Laws of Opposition.

Left to Right: Vertical Opposition, Horizontal Opposition (Middle of the board) and Diagonal Opposition at the bottom.

Not Shown: Distant Opposition. Place the White King on g2, and Black King on e8. Another Distant Opposition: White King a8, and Black King d7.

James Mason:
Propositions
I. The player who has the Opposition can always retain it.
II. If a player abandon the Opposition, his opponent can instantly seize it.
III. When there are 2 squares between the Kings the player with the move can instantly seize the Opposition.
IV. When there are THREE SQUARES OR MORE between the Kings, neither player can gain the Opposition, and the player attempting to do so will yield it to his adversary
V. The player with the Opposition cannot force his opponent to a side of the board, but he can go by him, while the latter cannot do so against the will of the former. Note, however, that in GOING BY, he loses the Opposition.
VI. Vertical Opposition cannot be changed into horizontal Opposition against the will of the adversary, nor conversely. But direct Opposition can be turned into diagonal Opposition ; and conversely.
VII. The DISTANT OPPOSITION cannot be retained. Each player can if he pleases seize it every time he moves.
VIII. The player with the move can always seize the distant Opposition, or of course the Opposition itself, if only two squares intervene between the Kings.
(This is virtually the same proposition as the preceding one).
IX. If on each move the Kings approach one another the player who started with the DISTANT OPPOSITION can advance last without yielding the Opposition to his adversary.
.......... bear in mind in actual play appear to be:
(1) You can gain the opposition on the mover or not at all.
(2) If you give it up, your opponent can seize and retain it.
(3) If the Opposition cannot be seized on the move, neither player can ever obtain it aginst his adversary's wishes, and attempting to yield it to the opponent.
(4) If you have the Distant Opposition, you can advance last without yielding the Opposition to your opponent.
British Chess Magazine, Vol. XIX, 1899.

I've always found this interesting:


White to move and draw.


White to move and win.

Black's king can move straight back in diagram 1, therefore he can draw.

The diagram above:
The Rule is for White to Win, there must be a check on the sixth rank, which of course Black having knowledge of avoids.
Another Preposition this time from Reuben Fine
"The rule is that if the White King is two or more squares in front of its pawn White always wins; if it is one square in front of it, White wins only if he has the opposition."
Of course there are exceptions. A rook pawn is always a draw if the Black King can reach c8/f8 b8/g8 or a8/h8. The King can never be driven out.

I remember seeing somewhere that you can force opposition away from an opponent. Which, I think makes rule #1 untrue. It is called tri-something, or something like that... It takes three moves. I wish I could remember the exact name.

I could be wrong... It happens.

Triangulation. You literally move your king (or other piece) in a triangle in order to reach a position that your opponent has to move instead of you. Here is a very simplistic example:

If 1 Kg3 then 1 ... Kg8, and if it was black's turn to move, White would win immediately. So therefore you need to waste a move, without changing the position. 2 Rf3 puts black in Zugzwang, but we want to learn about triangulation. So therefore you should play 1 Kg4! Kg8 2 Kg3, and White wins, since black has to move.

A more complex example:


If Black to move White wins by 1 ... Ke5 2 Ke3, and Black has to give up the pawn. But what if it's White's move? 1 Ke3 doesn't work because after 1 ... Ke5, White's King must step back. But if it were only Black's move in that position: 1 Kf2! e3+! (1 ... Ke5 2 Ke3) 2 Ke2! (2 Kxe3? Ke5, and White's king moves back; 2 Kf3 also wins) 3 Ke5 Kxe3, and White wins.

However, you often have to watch out for counter-triangulation. White triangulates his king in order to waste a move, so therefore Black just returns the move back by triangulating his king too. So therefore White must counter-triangulate. And so on and so forth...

I was just going over this in Reassess Your Chess, and now I am confused. Silman says if you are to move an there is an odd number of squares between kings your opponent has opposition. If you are to move with even number then you have it etc.

Look at Octal's positions above, where the kings have exactly one square between them. Whoever has the move in those positions has to move their king out of their opponent's way. Thus, the player NOT to move has the opposition.

--Fromper

Yes, I think that is what I was saying, though not in such a clear manner. What is confusing is the original post. I spent a good time on that chapter yesterday and I understand the rules Silman gives for who has the move and odd or even number of squares. Silmans information seems to contradict parts of the original post. But after going back over the exercise with kings on a1 and a8 with the white king trying to get to f8,g8,or h8 black can indeed take opposition from white, but he can’t prevent whites goal.

I am assuming you have the book Fromper. You recommended it in another thread if I am not mistaken.

Yes, Silman's a good author. One of these days, I need to get around to finishing reading his books.

--Fromper

Here is how I teach about opposition:
To gain the opposition, there are two rules to know:
1. Move to a square that is the same color as your opponent, and
2. If the kings are not on the same file or rank, chose the square by the "box" method. When you move into the same color square as the opponent, imagine that the kings form two corners of a box. Make sure that the all four corners of the box are the same color.

Thoughts?

Bela