Rook ending is the most difficult (and most frequently played) ending in chess. Theory behind it is tremendous. Philidor Draw, Lucena Win, Saavedra and Lasker Manoeuver (above diagram)
Lasker manoeuver ? Yes, Lasker Manoeuver maybe not as famous as his peers (Lucena, Philidor, Saavedra etc) but still it contain some fancy play.
Material is equal. Both pawns are one step away from promotion yet white, with a move in hand and slight advantage due to his king position which is nearer to his pawn, is able to pull a nice win here. 1. Kb7 Rb2 2. Ka7 Rc2 3.Rh5 Ka4
The whole manoeuver is repeated again.
4.Kb6 Rb2 5.Ka6 Rc2 6.Rh4 Ka3
7.Kb5 (error.7.Kb6! is correct as pointed out by Firdaus. Thanks Firdaus!) 7. ... Rb2 8.Ka5 Rc2 9.Rh3 Ka2
now comes the killer blow
10. Rh2 win!
This study was composed by Lasker in 1892 and what i like most about the manoeuver is it is only working if the chess board measurement is 8 x 8 (current measurement). Say if the board is 9 x 9 then the above manoeuver is no longer working!