What are the Endgame Principles?

Are there some principles or tips on these issues in the endgame:

-When and how to push your pawns
-Where to put your king
-How to treat a passed pawn
-Where to put your rook

In the opening and the middle game I sort of know what I am doing, but in the endgame I usually end up playing random moves with no clear idea what I am doing. For example see how I ruined this game:

With a 1695 blitz rating, you must certainly know many of the basics.

What were your expectations here? Your pawn structure was weak. Your knight was passive.

Forcing an improvement in your pawn structure seems a pretty clear idea.

You might even have been better.

/ / What endgame courses have you studied?

I know some basics but I can't use them properly. Most of the endgame instructions explain certain key positions, but I need a more general and practical knowledge. The problem is that in the endgame there are more possible moves and I can't really choose which one to play. For example I don't know how to handle a position where I have 3 pawns in the kingside against 2 pawns. When to move my king, when to push my pawns and which pawn to push.

I have read first chapters of Silman's book and some chess.com lessons.

Have you read at least the first five chapters? Maybe it would help to go farther. My rating is way below yours, but my guess is that, in your game, you were in trouble well before the ending. I suppose it depends on what one counts as the ending. I think that there are books with a focus on the transition from the middlegame to the endgame.

I think I have read the first five chapters. The problem is that the endgame needs a more general way of thinking and needs long maneuvers but I'm used to move by move thinking and searching for immediate tactics

I am too weak a player to do trustworthy analysis, but I would guess that this is a part of the game that creates the potential for serious endgame difficulty. I would also guess that you already know enough endgame stuff to see that for yourself. Were you thinking much about future endgame issues during this part of the game?

You're right. I should have noticed my doubled pawns. I guess on move 18 I could start putting my pawns on light squares with 18. ... c4  to keep them from the threat of the Bishop, but this idea didn't come to my mind during the game.

This is really an area where I do not have much in the way of qualifications. There are books about the middlegame-endgame transition, but I would guess that it would currently be appropriate to do more Silman reading. Somewhere around chapter seven of the endgame book, I think that Silman starts getting into positions with bunches of pieces and pawns. Perhaps it would also be helpful to look at the Reassess book. For one thing, there is a lot about bishop-against-knight issues. I think doubled pawns are in there two.

"... I like [Shereshevsky's 'Endgame Strategy'] a lot, but it has more to do with transitions from the middlegame than with endings themselves." - IM John Watson (2000)
http://theweekinchess.com/john-watson-reviews/endings-endings-endings

https://www.chess.com/article/view/quotendgame-strategyquot-by-mikhail-shereshevsky
"... The second part of [The Shereshevsky Method] is a concentrated version of Endgame Strategy, ..."
https://www.newinchess.com/media/wysiwyg/product_pdf/9056.pdf

https://chessbookreviews.wordpress.com/tag/mikhail-shereshevsky/

It's actually a lot like the opening and middlegame in the sense that pushing pawns can be a big weakness if your pieces can't support them. First focus on making your pieces as active as possible. Afterwards you can consider pushing pawns.

In the endgame active pieces (which includes your king) are extremely important. In the middlegame you can live with one bad piece, but in an endgame it can mean it's time to resign already.

Kings love to infiltrate in the endgame.

If you're unsure where your king belongs, bring it to the center as fast as possible. That's usually a good start.

Passed pawns are good as decoys. When they pull enemy pieces away, you can infiltrate with your pieces.

They're also good as queens  but remember they need support, so first focus on making your pieces (which includes your king) as active as possible.

In general, in the endgame pieces want to be able to attack weak enemy pawns. If you have a rook (or knight, or bishop) that is completely unable to eventually attack a weak enemy pawn, then often you have no chance of winning that endgame.

So a rook wants to be on an open file... if that file can be used to infiltrate and attack weak pawns. Rooks are also good behind passed pawns (but if they have very little scope, consider placing them beside the pawn). Rooks are also good on open ranks where they shift back and forth, forcing enemy pawns to move, which will often create weaknesses.

Of course rooks are also good at cutting the enemy king off along a rank or file.

in endgame, put your rook behind your passed pawn.