Point Count Chess, NO.15C, p32
Example Sequence

After gaining the Advanced Chain at K5 (e5), as seen in No.15B, H&M-S turn White's focus to bringing forward the f- & g-Pawns (f2-f4, g2-g4, f4-f5), ready to attack Black's Kingside position.

The potential benefit to White, could be any of the following:

1. Gives Black a Compromised King-side (should Black Castle O-O).
2. Open a file through which White may attack and invade.
3. Weaken Black's Pawn structure on the Kingside.

The primary benefit, to White, comes from what H&M-S say is "the known fact that a cramped pawn wing usually needs more pieces for defense than for attack, because the cramp prevents the defenders from operating at full capacity."

Beneath the ChessFlash viewer, you'll find my analysis of the position featured in Point Count Chess:
1. PCC, p.32, No.15C, after 16...Ne7
2. Result of Capitalizing an Advanced Chain.
3. Summary of Capitalizing an Advanced Chain.

My Analysis

Position #1, My Analysis
PCC, p.32, No.15C, after 16...Ne7

After: 1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Be7 5.e5 Nfd7 6.Bxe7 Qxe7 7.f4 a6 8.Nf3 c5 9.dxc5 Nxc5 10.Bd3 Nxd3+ 11.cxd3 Nc6 12.Qd2 O-O 13.O-O Bd7 14.Rf2 Qc5 15.Rc1 Qa7 16.d4 Ne7

After: 16...Ne7

1. The French Defence (Main Line), Leads to White's

See No.15A for more details regarding the build-up to White's Advanced Chain. Here, in No.15C, I'm just going to recap in brief, to get quickly to the main focus of this example: Capitalizing an Advanced Chain ...

 The Advanced Chain,Capitalizing an Advanced Chain, After 1.e4 e6 2.d4 d5 After 1.e4 e6 2.d4 d5, the game reaches the Main Line, of the French Defence.
 The Advanced Chain,Capitalizing an Advanced Chain, After 4.Bg5 Be7 5.e5 After 4.Bg5 Be7 5.e5, White gains the Advanced Chain at K5 (5.e4-e5), following White's Pin on Black's Nf6 (4.Bc1-g5) and Black's counter measure, developing his dark-Bishop to cover his Queen (4...Bf8-e7).

2. The Immediate Aftermath of White's Advanced Chain at K5 (e5)

 The Advanced Chain,Capitalizing an Advanced Chain, After 5...Nfd7 6.Bxe7 Qxe7 After 5...Nfd7 6.Bxe7 Qxe7, Black's King Knight is forced to flee from its favorite square (5...Nf6-d7), paving the way for the dark-Bishop exchange (6.Bg5xe7), which Black's Queen completes (6...Qd8xe7). That completes the moves as seen in No.15A and No.15B. Now, we're into No.15C and the extended sequence that shows how White can Capitalize on his Advanced Chain ...

3. White Mobilizes his f- & g-Pawns, for a Kingside attack

This is the part where H&M-S turn White's focus to bringing forward the f- & g-Pawns (f2-f4, g2-g4, f4-f5). It doesn't all happen in one go, and White must be patient, as he attempts to bring these two Pawns forward, as part of the overall attack against Black's Kingside position.

The Result, below, shows the outcome of White's Kingside Pawn advance.

 The Advanced Chain,Capitalizing an Advanced Chain, After 7.f4 After 7.f4, White mobilizes his f-Pawn, bringing it immediately to the front line (7.f2-f4), where it forms part of the base of White's Advanced Salient (d4,e5,f4).
 The Advanced Chain,Capitalizing an Advanced Chain, After 8.Nf3 After 8.Nf3, note that White has waited until his f-Pawn has been positioned into the Advanced Salient, before developing his King Knight to its favorite opening square (8.Ng1-f3). Had White developed his King Knight earlier, he would have had to move it a second time, in order to develop his f-Pawn to where it currently sits, and that would have wasted precious Tempi (more than one Tempo, and quite possibly ruining White's Kingside attack.
 The Advanced Chain,Capitalizing an Advanced Chain, After 8...c5 9.dxc5 Nxc5 After 8...c5 9.dxc5 Nxc5, Black's c-Pawn attacks the Queenside base of White's Advanced Salient (8...c7-c5), resulting in a Pawn exchange on c5, which removes White's d4-Pawn (9.d4xc5). White's Advanced Salient has been dissolved into just an Advanced Chain (f4,e5). Black's Knight completes the trade (9...Nd7xc5), bringing it into range for the next Minor Piece exchange, which ends with White's c-Pawn coming across to the d-file (through which White will regain his Advanced Salient) ...
 The Advanced Chain,Capitalizing an Advanced Chain, After 10.Bd3 Nxd3+ 11.cxd3 After 10.Bd3 Nxd3+ 11.cxd3, White brings the c-Pawn to the d-file (to re-establish the Advanced Salient), as he trades his light-Bishop for Black's Nc5 (10.Bf1-d3 Nc5xd3+ 11.c2xd3). White has now traded both Bishops off the board, in order to remove Black's King Knight and dark-Bishop (the latter could threaten White's Advanced Chain or Advanced Salient, as they're on the dark-squares).
 The Advanced Chain,Capitalizing an Advanced Chain, After 12...O-O 13.O-O After 12...O-O 13.O-O, both Kings Castle Kingside, but it's Black who has Castled into trouble, en route to his defeat.
 The Advanced Chain,Capitalizing an Advanced Chain, After 14.Rf2 After 14.Rf2, White's King Rook is moved one step forward (14.Rf1-f2), taking it off the light-squares and onto dark-squares. I think this is due to the presence of Black's light-Bishop, and the intention of White to push his d3-Pawn onto d4, which would open up a channel of attack, down the light-squares to f1. The importance of White's King Rook cannot be underestimated, as it's used in White's Mating attack, to win White the game.
 The Advanced Chain,Capitalizing an Advanced Chain, After 16.d4 After 16.d4, White regains the Advanced Salient, as his replacement d-Pawn (formerly the c-Pawn) is pushed to d4 (16.d3-d4), re-establishing White's Advanced Salient (d4,e5,f4). The move also blocks the attack by Black's Queen, on White's Rf2, along the a7-g1 diagonal.
 The Advanced Chain,Capitalizing an Advanced Chain, After 17.g4 After 17.g4, White mobilizes his g-Pawn, bringing it immediately to the front line (17.g2-g4), to sit in Phalanx formation, alongside the f4-Pawn. With this move, White prepares for the second advance of his f-Pawn, so it can attack Black's e6-Pawn (currently forming Black's Pawn Chain, trying to resist the advance of White's Center Pawns).
 The Advanced Chain,Capitalizing an Advanced Chain, After 22.Nxf7 After 22.Nxf7, White sacrifices his King Knight to remove Black's f-Pawn (22.Ng5xf7), giving Black a Compromised King-side.
 The Advanced Chain,Capitalizing an Advanced Chain, After 23.f5 After 23.f5, White makes the second advance of his f-Pawn (23.f4-f5). White has completed the recommendation by H&M-S, for Capitalizing an Advanced Chain: bringing forward the f- & g-Pawns (7.f2-f4 » 17.g2-g4 » 23.f4-f5), ready to attack Black's Kingside position. The final phase of the plan leads to White's victory, by Checkmate, which is shown in the Result, below ...

The Result of Capitalizing an Advanced Chain...

 (RESULT) The Advanced Chain,Capitalizing an Advanced Chain, After 24.fxe6+ Kxe6 After 24.fxe6+ Kxe6, White exchanges his f-Pawn to remove the base of Black's Q4 (d5) Chain. Incidentally, the capture by White's f-Pawn (24.f5xe6+) also launches a Discovered Check, which also "Double Checks" Black's King. Black chooses to capture White's Pawn, with his King (24...Kf7xe6), completing the Pawn exchange, while also getting Black's King out of the firing line -- unfortunately, this also puts Black's King into an alley, where he has no escape!
 (RESULT) The Advanced Chain,Capitalizing an Advanced Chain, After 25.Qxh6+ gxh6 After 25.Qxh6+ gxh6, White sacrifices his Queen (25.Qe3xh6+ g7xh6), as part of his Mating attack.
 (RESULT) The Advanced Chain,Capitalizing an Advanced Chain, After 26.Rf6# After 26.Rf6#, White's King Rook Checkmates Black's King, on f6 (26.Rf2-f6#), completing a successful attack by White, following the creation of his Advanced Chain at K5 (5.e4-e5). Looking at the diagram (left), White's Advanced Chain plays two roles in his Mating attack: It supports the King Rook, as it comes up to attack Black's King (26.Rf2-f6+); It prevents Black's King escaping, via d6.

Summary of Capitalizing an Advanced Chain...

The Summary for the build-up to White's Advanced Chain at K5, can be viewed here.
1. White patiently brings his f- & g-Pawns forward, to join in an attack against Black's Kingside (note: Black's King must Castle Kingside, for this all to be worthwhile, for White).

2. White first brings his f- & g-Pawns together, in Phalanx formation, on the fourth rank (7.f2-f4 & 17.g2-g4).

3. White sacrifices his King Knight, to remove the base of Black's 3-Pawn Chain (22.Ng5xf7).

4. White's f-Pawn is used to take-out Black's e6-Pawn. In successive moves, it is advanced a second time, into an Advanced position (23.f4-f5), before capturing across onto e6 (24.f5xe6+).

5. White's g-Pawn never moves beyond its current position on g4 -- well, not in this example, as it plays a key role in ensuring Black's King cannot escape from Checkmate.

6. White's King Rook Checkmates Black's King, (26.Rf2-f6#). Having Castled onto the f-file, earlier (13.O-O), White's King Rook never leaves the f-file, as it plays an integral part in the successful Mating attack, together with White's Advanced Chain at K5 (e5).

PGN

[Event "PCC, p32 Diagram NO. 15C"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "Horowitz"]
[Black "Mott-Smith"]
[Result "1-0"]
[PlyCount "51"]

1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 Be7 5. e5 Nfd7 6. Bxe7 Qxe7 7. f4 a6 8. Nf3 c5 9. dxc5 Nxc5 10. Bd3 Nxd3+ 11. cxd3 Nc6 12. Qd2 O-O 13. O-O Bd7 14. Rf2 Qc5 15. Rc1 Qa7 16. d4 Ne7 {PCC, p32 Diagram NO.15C} 17. g4 Rac8 18. Rd1 Rc4 19. Qd3 Rfc8 20. Ng5 Ng6 21. Qe3 h6 22. Nxf7 Kxf7 23. f5 Ne7 24. fxe6+ Kxe6 25. Qxh6+ gxh6 26. Rf6# 1-0

End.