The position I want to present is an example of complexity of the chess game. Some of the moves that follow may seem beyond human imagination. Also, this is a kind of position that is very good suited for improving one's abilities to calculate variations. I use this method with many of my students and it seems to work - they are able to calculate longer variations with greater precision.
Now, if you want just to watch a nice combination then you can simply go through all the variations. If you want to get some practice, though, you should approach this exercise in the following way. Each time you see a new diagram ask yourself "How would I play here?" Give it some thought. Then compare your findings with analysis in the text and move towards the new diagram. Also, if you think that something is wrong in the analysis - feel free to ask questions. I will be more than happy to answer them. You might want to take a chess board and put the positions you see on diagrams on the board since the questions asked are pretty challenging.
So, let's go, the starting position is:
The only move that leads to an advantage, even more - to a full point, is 1.g5!!
In all other lines black has better chances. Here are some possible continuations: 1.Ng3 Rfc8.2.Nf5 Bxf5.3.gxf5 b5 and black is better; 1.e5 Rxe5.2.Ne4 Rxe4!.3.g5 (3.fxe4 Bxg4 -/+) 3....Nh5.4.fxe4 Qxa2.5.Ng3 Qa1+.6.Kd2 Qxb2.7.Nxh5 gxh5.8.Qxh5 Qg7 and black should win; 1.Nf4 Rfc8.2.g5 Rxg5.3.Rd5! Rxd5.4.Nfxd5 Bxd5.5.Nxd5 Qd8.6.Nxf6 exf6.7.Qxh7 Kf8 and black has at least equal chances because there is no way white can get to the black king.
Now, black is forced to take on g5 because after 1....Nh5.2.Nf4 Rxg5.3.Ncd5 Bxd5.4.Qxg5+- white easily wins. So, 1....Rxg5 is the only move. Now you should think for a while. I give you a hint - look at the entire board to find the solution!
This is the point! Truly, a beatiful move! Black cannot take on b4 because his rook hangs. So he has two possibilities. If black plays 2....Rh5 then after 3.bxa5 Rxh6.4.Rxh6 Nh5.5.Rd1 Kg7.6.Rxh5 gxh5.7.Rh1! white should easily win. The question is what should white play after 2....Qa3+ Where should the king go, to d1 or to d2? Take another moment to think about it.
This is the move that wins! Another option, 3.Kd2, leads to a position where black has some compensation for sacrificed material: 3....Re5.4.f4 (4.Nd5? Rxd5.5.exd5 Qxb4+ and black wins. This is the main difference between 3.Kd1 and 3.Kd2 - when the king is on d1 black cannot take on b4 with check and white simply wins bishop on e6!) 4....Qxb4.5.fxe5 dxe5. Black has four pawns for the rook and in addition white king is very unsafe. Black wants to take on e4 or play Bc4 in the next move, and so he has certain compensation. Now let;s see what happens after 3.Kd1:
3....Bc4. Other moves lose immediately: 3....Re5.4.Nd5 Rxd5.5.exd5+-; 3....Rh5.4.Rxh5 Nxh5.5.Nd5+- In both cases white uses the unlucky position of black queen on a3. Now you have next problem to solve: how should white play after 3....Bc4?
A brilliant move! White can certainly take the rook on g5, but surprisingly is the position after 4.Qxg5 Bxd3.5.cxd3 Rc8.6.Qc1 Qxb4 not clear at all - black has three pawns for the knight and strong initiative in addition.
5....Rh5 (After 5....Rxe5.6.Ne4 or 5....Bxd3.6.exf6 white wins easily).6.Rxh5 Nxh5. Now it's your turn again - you need to find the final creative idea to finish the game.
This kills black! The knight goes to g5 and black is helpless again checkmate. 5....Bxd3.6.Ng5! and now enjoy the rest:
6....Bxc2+ (6....Bxe2+.7.Kxe2 Ng3+.8.Kd1!! [8.Kf2 Qe3+!!.9.Kxe3 Nf5+ and 10....Nxh6 -+] and white wins) 7.Ke1 Qxb4+.9.Kf1 Ng3+.10.Kg2+- with checkmate in next move.
This completes the exercise. I hope you enjoyed it and please ask questions if you have any! Good luck!