Recently, I have put much effort into learning the endgame KQ vs. KR. This is probably the most difficult chess endgame to study. Many moves are counterintuitive compared to other endgames where you crowd the enemy king until you get forced checkmate.
It tempting in many positions to check horizontally or vertically. This is often wrong, and the correct procedure is to check once or twice along a diagonal before checking horizontally or vertically. In some positions, the best move is to not check but attack the squares around the opponent's king. To win, you have to be able to calculate well.
Against a good defense, there is a desired position that you must reach to separate the King and Rook. I note this position on the web page below.
This is also the kind of ending that you might only see twice in a lifetime. Because of the difficulty, studying it might not be time well spent. You cannot learn it overnight or just through general principles.
However, I want to be prepared for it.
I have created 33 study positions on the webpage below. These start with the easiest and progress gradually to the more difficult. Most problems build upon the ones that came before them.
If you are interested, scroll down until you see "KQ vs. KR" on the right side.
This is not yet complete. I plan to add more positions regarding the "3rd rank defense" and how to push the enemy king to the corner.
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