How to analyse multi-pawn endings like this?

Thank you in advance!

Pawn endgames like this are mostly about understanding King Opposition and which pawn endgames are winning due to the key squares for the pawns. After the player knows those nuances from study, then it is simply a matter of calculation. I'll show a few lines here which show how black is winning, but the player would have to visualize most of these ideas mid-game before moving.

Then after I show those lines in a pgn diagram, I'll link a video on understanding those fundamentals for the pawn endgame (King Opposition and the key squares).

Hi, how to find this move when you are playing this kind endings?

Is there any theory?

@sta202020 other than those fundamentals I shared in the video, there isn't really "theory" other than certain endgame concepts which usually work; these are the things which require study to learn.

The short answer is you find moves like what I shared by studying lots of endgames (learning) and playing many endgames (experience). You also don't always have to be able to calculate start to finish. If you can accurately visualize that, then awesome, but in many positions, you can also navigate pretty well just by visualizing far enough to the next mental checkpoint you identify is still winning for you.

Pawn endings are a matter of calculating.

Understanding opposition and key squares is very important, but in these simplified positions there is simply no substitute for calculation. You have to be able to count! Luckily, these simplified positions are also the easiest (but not easy!) to calculate. It will e difficult at first, but working on your simple calculation skill will pay enormous dividends

you mean one should calculate many lines before you find the correct move?

@7

You should calculate all feasible moves and all the way deep.
There is a book titled The Final Countdown by Hajenius & van Riemsdijk on it.

Thank you for your recommendation,did I get the right book?

@9

Right.