Perhaps a stronger player can tell me what went wrong in this game

I know that coaches usually say to analyse the game first without the help of an engine. I think I had a rather good position in the opening but I gave up my advantage to get a very bad position. My opponent could make a perpetual but missed it. I was at the end a pawn up, but I could not see how to improve the position. Perhaps some of you guys can give me some tips about the mistakes I did.

You are of course right about 10.Nd2 and about g3 to prepare f4.  After 11.f4 I saw that my position was awful, giving black a strong initiative.

I agree with @UzayAltay and will just comment on the endgame. Fixing his pawns on light squares was good because you have a knight vs his light squared bishop. At the end you have a win. Look at the position and you see you want your knight at b5, e4, or f7 to force the king away (especially b5 to make the knight defended). First, put your king to d2 to protect b3. Next, play nc1 ne2 and then  probably to g1-f3-g5 (or even c3-b5). Then, you might even consider nh7-f6 and your knight infiltrates. Eventually you may have to bring in your king and sac-b3 but you are certainly winning.

As you noted in #4 the Nd2 was a pain.  Your game was shaking after that, I am not so against 11. f4 because it takes a great sense of will to play say 11. Nf3
You finally we able to do that on 20. Of course you had been playing without queen's bishop all game long.
At 36. you should have been looking for a [solid] outpost for your knight, I looked at Nf4 (I see you saw that route) but more Nc3/b5
At 38. ... g5 maybe, trying to box the bishop into the black side of the board. Without the boxing and the rook I am starting to struggle to find a line.
At 45. It might have been possible to play ... Nf2 ( as a first move towards Nb5 [really] ) because you have the problems of white attacking the b-pawn with bishop and the g-pawn with the king.

@suspicious_openings yeah, you just cannot be weak on both sides of the board when you have knight v bishop.  It is almost possible to argue that without the passed pawn, white would be bust.

From the final position, let's try this:

1. Ne1 Bg4 (1...Ke5 2.Nf3+ Kd6 is equivalent) 2.Nf3 Bf5 3.Kf4! Bc2 4.Nd2. Now if black moves the king, white invades with 5.Ke5. What looks like toughest defense is 4...Bd1 5.Kg5 Bc2 6.Kf6 Bd3.

This is as far as white can get without sacrificing pawns. So now it's time to start sacrificing. 7.Nf3 Bc2 8.Ne5 Bxb3 9.Nf7+! Kd7 (not 9...Kc7? Ke7 +-) 10.Kxg6 Bxa4 (not 10...Bxc4? 11.Ne5+ +-).

After this it's not clear, at least to me doing this in my head without a board. Pawns are equal, and each side has one passed pawn and one extra but backward pawn. You have to calculate precisely, and I can't do it beyond this point in my head.

But the point is white can definitely try for a win. It's possible I missed something better along the way.

Where did you go wrong? You just traded the pieces with no purpose. And you reached a bishop vs horse very difficult endgame if not a draw. You should have atleast kept your rooks and minor pieces. You should trade down to an endgame only when you know that it's a won endgame.

1. Ne1 Bg4 2. Nf3 Bf5 3. Kf4 Bc2 4. Nd2 Bd1 5. Kg5 Bc2 6. Kf6 Bd3 7. Nf3 Bc2 8. Ne5 Bxb3 9. Nxf7+ Kd7 10. Kxg6 Bxa4 --- Line proposed by FM chuddog.

Maybe black goes 1. ... Ke7 2. (Kf4 or Nd3) Kf6

N against B isn't easy with pawns on both sides of the board. Maybe you had a win at the end and maybe not. In any case, you shouldn't have swapped off to the N vs B ending. All told I thought you played planlessly. Although you achieved a big position, your pieces seemed uncoordinated.

I preferred 6. d5. After that move, I think white gets a better advantage than you achieved.

Even so. after 6. d5, white is looking better. 6.d5 should have been an obvious move so there isn't much need to look further into the game. I certainly didn't like the knight retreat, blocking in the bishop on c1. Presumably it was played to enable f4, but f4 was a poor move which helped black. White's game went downhill badly from Nd2. Possibly a winning position was attained at one stage .... but that's immaterial because if so, it was the result of a bad blunder by black.

I would have played f4 in the opening btw, before Nf3. I usually play that way against the extremely dubious defence that black employs in this game. White has so many opportunities to attack in the centre, often by sacrificing a pawn.

It was a Daily Game, so I took a lot of time to analyse the endgame (without engine, of course). It is what you said, I cannot improve my position. The problem is that I cannot allow black to take my pawns on the kingside, the game would be simply over for me. The problem is that somebody has to cover the kingside, or the knight or the king. 

#24 Look at #16 and #19

This is good! I just didn't calculate further after I saw that the bishop would begin to take my pawns on the kingside. In my calculations black could just make waiting moves forever with the bishop. I see now that I was wrong. I should perhaps try this, although I am still afraid that the bishop would be more useful than a knight in the position after 57...Bxa4. 

But this is not the question. The question is: why I didn't see this variation? I don't know, I though I tried everything.

Almost all whites moves can be improved? You mean things like 1.e4 instead of 1.d4 or things like that?

I checked the line with the engine, and it doesn't work, my best attempt is a draw. After 57. Kxg7 white is lost. Black will first attack my knight with 57...Ke7 (and not take a pawn with the bishop) and after 58. Nh6 Bxc4 59. Nf5+ Kd7 the game is over (-2.25).

As a general rule, the side with more space does not want to trade off all their pieces.  I think avoiding some of those exchanges and relocating your material so you could have leveraged your pawn breaks at some point is probably what most high rated players would have done in the middle game after you got all that space.  I agree your opening seemed to reach a favorable position, but you just kind of let your opponent follow through with his plan of liquidating the material so that the space meant very little.

I think I didn't take the game seriously until I saw that things were not going well. From this moment I began to think longer, but without much success. 

• Hey that's not what I said; I said "you have been 'Berned' (as he is from Bern) and that DRAW  is a great result."  I have no engine, don't want or need one, and will never use one.  Why don't you think for yourself in chess as you have in your education?  Your opponent at 1250 no way in Hades played that game himself.  (Maintaining cd tension, fe tension, perfect defense, Bc8, Qh4, please itsitas obvious as anything, look at his other ratings and game history.  's another note since science is politicized (see Thomas Kuhn, the structure of scientic revolution) funding and Grant money can best be found singing praise only of th status quo, not actually creating new hypothoses.  Good luck polyglotting.