[Event "Beginner: Curriculum <--- START HERE: The Endgame"]
[Site "https://lichess.org/study/Ztgx3vJq/Vooa3887"]
[Date "????.??.??"]
[Round "?"]
[White "?"]
[Black "?"]
[Result "*"]
[Annotator "https://lichess.org/@/jomega"]
[ECO "?"]
[FEN "5k2/8/8/8/8/2P5/8/3K4 w - - 0 1"]
[Opening "?"]
[SetUp "1"]
[UTCDate "2018.12.03"]
[UTCTime "15:49:46"]
[Variant "Standard"]

{ The old masters insisted that after learning the rules of chess the next step was to practice the elementary endgames. Why? Because you'll need to know these, they reinforce the previous rules, they build up your visualization of the board, they allow a simple situation to introduce new topics, such as tactics, and they are simpler than other topics because of the few number of pieces.

There are other approaches to learning those new topics. Talk to your mentor about what would be best for you.

The approach taken here is to cover the endgame in approximately the order of difficultly but categorized by type to make it easier to find what you are looking for.

Endgames
https://lichess.org/study/vMmllPNw

In the given position it is clear that White is the only one with winning chances, and to win he will have to queen his pawn. The pawn cannot simply move up the board by itself as Black will just capture it. Hence, White will have to control the queening square c8 to win. That is, White must play to occupy either b7 or d7 with his King. It is White's move. He has five King moves and one pawn move from which to choose. With best play by both sides, one of those moves wins and the rest draw! Do you know how to figure out the answer?

For completeness sake, I present the solution here though the concepts to understand the position are not presented until later.
- } 1. Kc2 $1 { People that only learn the concept of opposition might think that 1.Kd2 (all four corners of the rectangle (d2,f2,f8,d8) are the same color) is the winning move. Unfortunately, as I've pointed out earlier in the course, sometimes you want the opposition and sometimes you do not.
The concept of key-squares, together with knowledge of simpler King and Pawn versus King endgames, gives the solution. } ( 1. Kd2 $2 { Taking the opposition here only draws. } 1... Ke7 2. Kd3 ( 2. Ke3 { Continuing to take the opposition. } 2... Kd7 3. Kd3 { Yet again White takes the (distant) opposition. } 3... Kc7 $1 { All the other King moves lose to best play! Those who subscribe to the opposition theory alone would claim that the problem is that White cannot now play Kc3, which would maintain the distant opposition. Also, clearly, Ke3 does White no good even though that takes the opposition.
This is all true, but this does not seem to me to be the best way of understanding what is happening in the position. } 4. Kd4 Kd6 $1 { The only move that holds the draw. } 5. Kc4 Kc6 $10 ) 2... Kd7 3. Kc4 Kc6 $10 ) 1... Ke7 2. Kb3 Kd6 ( 2... Kd7 3. Kb4 Kd6 { Black is trying to get White to make an incorrect move. } 4. Kb5 $1 { The only winning move. } 4... Kc7 { Black tries to control b7 and d7. } 5. Kc5 $1 { The only winning move. } 5... Kd7 6. Kb6 Kc8 { Still trying to control the key-squares. } 7. Kc6 $18 { White wins this position regardless of whose move it is and regardless of whether his pawn is on c2, c3, c4 or c5. Knowing such things makes it much easier to play King and Pawn versus King endgames. } ) 3. Kb4 Kc6 4. Kc4 $18 { White will now be able to occupy b5 or d5 (a turning maneuver) and from there occupy either b7 or d7. The pawn will queen and White wins.
We will cover these ideas in the endgame of King and Pawn versus King. } *