Why choose to study a game that occurs about 1 in every 1200 games?
After searching for something that wouldn’t take long I realized that this endgame cannot be mastered quickly. In my pursuit, I found chessable.com which has a fifteen chapter course on the Queen vs. Rook endgame!!
Again, why would one want to go through such a course for a 1 in 1200 chance at using it? While I just have a thirst to master any and everything in chess, I think there is valuable lessons in simply how the rook and queen can battle each other across the board.
For the rest of you out there who may like the smallest tidbit of knowledge about this game, I would recommend learning the Philidor position with black to move and also how to get to the Philidor position with black to move if it is white to move instead.

That is covered in chapter 2 and is essential.
If it white to move and you want this position with black to move, you can do this in a few ways. Here is one.
- Qe5+ Ka7 or Ka8 (since 1 … Kc8 2 Qe8# and 1 … Rc7 2 Qxc7+ with mate to follow) 2. Qa1+ Kb8 (since 2 … Ra7 3 Qh8#) 3. Qa5
Now, you’re in the above position with black to move. There are several options, some lose quicker than others. All are worth studying, the hardest ones being those when the rook moves to b3, b1, f7, or h7.
Anyway, the main purpose of the post is to introduce you to the valuable chessable.com resource which has several courses that may go into much more detail than what you can find on chess.com or lichess.org.