How would you evaluate this king and pawn endgame for white, and what's the best book to study King and pawn endgames? I would  like to learn more tricks and ideas behind these complicated endgames. For example, here is a game I played where I got into one (I was playing white).

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[Startply "83"]

1. e4  e6 2. d4  d5 3. Nd2  Nc6 4. Ngf3  Bb4 5. c3  Ba5 6. exd5  exd5 7. Bd3  Nf6 8. O-O  O-O 9. Nb3  Bb6 10. Bg5  Qd6 11. Re1  h6 12. Bh4  Bd7 13. Bc2  Bg4 14. Qd3  Bxf3 15. Qxf3  Rae8 16. Qf5  Ne4 17. f3  g6 18. Qh3  Nf6 19. Bg3  Qd7 20. Qxh6  Ne7 21. Qg5  Nh7 22. Qd2  c6 23. Bf4  Nf5 24. a4  Ng7 25. a5  Bc7 26. Bxc7  Qxc7 27. Nc5  Ne6 28. Nxe6  Rxe6 29. Rxe6  fxe6 30. Bxg6  Qg7 31. Bxh7+  Kxh7 32. Re1  Qg6 33. Re2  Rxf3 34. Qc2  Qxc2 35. Rxc2  Re3 36. Kf2  Re4 37. Re2  Rf4+ 38. Kg3  Rf6 39. b4  b6 40. axb6  axb6 41. Rf2  Rxf2 42. Kxf2  Kg6 43. Kf3  Kf5 44. h4  e5 45. g4+  Kf6 46. Ke3  e4 47. Kf4  Kg6 48. Ke3  Kf6 49. Kd2  Kg6 50. c4  Kf6 51. b5  cxb5 52. g5+  Ke6 53. c5  bxc5 54. dxc5  d4 55. g6  e3+ 56. Kd1  b4 57. c6  b3 58. c7  Kd7 59. c8=Q+  Kxc8 60. g7  Kc7 61. g8=Q  b2 62. Qc4+  Kb6 63. Kc2   1-0


Was this king and pawn truly won for white or did my opponent miss something? How could I have played better in the endgame?
There were a lot of inaccuracies by both players, I don't think you were ever losing, but you certainly threw away the win occasionally. I think three concepts might be helpful to you:


A protected passed pawn is very strong in a pawn endgame because it forces the enemy king to keep an eye on it at all times. Therefore allowing 46…e4 was a big mistake that turned an easy win into a draw. Instead take on e5, play h5 and h6 and then round up the black pawns.
Two connected passers are even stronger, because basically that's a dynamic duo of protected passers: The enemy king can never take the more backward one, because the other one will queen. And whenever possible, they will advance. See again move 46. If you take on e5 and black retakes with his king, you can fearlessly advance because as soon as the black king returns to g6 to attack the h6-pawn, you just protect it with g5.
The king is often curiously helpless against two pawns that aren't even connected and just one square apart: That's why 50.c4 was another big mistake. If black takes this pawn, there is no way for you to get at either the e- or the c-pawn. So 50…dxc4 51.Ke3 c3 and you cannot take on e4 because the c-pawn will queen. (Edit: Dag points out that after dxc4 b5 might still win for white, so maybe it wasn't a mistake, but the concept is still useful. Instead of dxc4, b5 should draw for black.)