> what now? how can i force his king to move away from the key squares? I do not understand endgames well enough to solve this.
g6 and you win. You can't promote the a-pawn. It's just there to keep the black king on the queenside. If he stays there, there's no way to force him out. This is indeed a typical strategy for this type of endgames.
Are you familiar with K+p vs K endgames? If you are, that should already answer your question. Rook pawns don't do well.
I've been reading Capablanca's "Chess Fundamentals" and even though i am still not versed well enough in chess to successfully read that book, with a lot of effort, much concentration, and a chess set, i can very slowly understand his examples and advices. Having said that, there is one example in the very first chapter that i just can't solve the way the author intended. Here is the example (all annotations are copied from the book):
Quote from the author after the last move:
Now it is time to go to the other side with the King, win the black pawn and Queen the single pawn. This is typical of all such endings and should be worked out by the student in this case and in similar cases which he can put up.
So the author want's us to solve it by going with the king for the a5 pawn and then queen the a4 pawn. I simply can't find the solution. I even tried against the computer here and used only hints - i simply can't find the combination which queens the a pawn