Attacking the Two Knights' Defence

There are three main ways you can try to attack against the Two Knights' Defence.

(A) 4.Ng5 is the most obvious, but I don't recommend it.  White can win a pawn, but if Black knows the book moves, you will have to defend against very active Black pieces.

e.g. 4.Ng5 d5! 5.exd5 b5!? 6.Bxb5 Qxd5

4.d4 is the move I recommend.

(B) There is a fun line which Black can equalise against but it's White who is attacking: Max Lange Knight Variation

4.d4 exd4 5.O-O Nxe4 6.Re1 d5! 7.Bxd5! Qxd5 8.Nc3! e.g. 8..Qa5 9.Nxe4 Be6 and now 10.Neg5 or 10.Bd2

(C) Max Lange Attack: This is another fun line which is very sharp and both sides are under attack!  Black may even be better in the long main line...

Smerdon,D - Heidenfeld,M [C55]
Australian Open Canberra AUS (11), 09.01.2001

1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.0-0 Bc5 6.e5 d5 7.exf6 dxc4 8.Re1+ Be6 9.Ng5 Qd5 10.Nc3 Qf5 11.Nce4 0-0-0 12.g4 Qe5 13.Nxe6 fxe6 14.fxg7 Rhg8 15.Bh6 d3 16.c3 d2 17.Re2 Rd3 18.Qf1 Qd5 19.Rd1 Be7 20.Qg2 Ne5 21.Rexd2 Nf7 22.g5 Nxh6 23.Rxd3 cxd3 24.gxh6 Qh5 25.Rxd3 Qxh6 26.Rg3 Bh4 27.Rg4 Qc1+ 28.Qf1 Qh6 29.Qc4 Rxg7 30.Nc5 Qf6 31.f3 e5 32.Rxg7 Qxg7+ 33.Kf1 Qe7 34.Qg4+ Kb8 35.Nd7+ Ka8 36.Nf6 1-0

...but often loses long before:

1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.O-O Bc5 6.e5 d5 7.exf6 dxc4 8.Re1+ Be6 9.Ng5 Qxf6? 10.Nxe6 fxe6 11.Qh5+ Qf7 12.Qxc5

When your opponents all know the long main lines of the Max Lange, you can turn to the Modern Variation:

(D) 4.d4 exd5 5.e5

4.d4 exd5 5.O-O Bc5 6.e5 d5 7.Bb5

This is a calmer way to play for a win, badgering Black about weak pawns.

e.g. Doghri,N -Matsuo,T [C56] Yerevan (7), 1996
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.e5 d5 6.Bb5 Ne4 7.Nxd4 Bc5 8.Be3 Bd7 9.Bxc6 bxc6 10.Nd2 Qh4 11.Nxe4 Qxe4 12.O-O Bb6 13.Re1 Qg6 14.Nb3 O-O 15.Bc5 Rfe8 16.a4 Bf5 17.Rc1 Rab8 18.Re3 Bxc5 19.Nxc5 Rxb2 20.Qd4 Rxc2 21.Rxc2 Bxc2 22.h3 a5 23.Kh2 Bf5 24.Rg3 Qh6 25.f4 g6 26.Nb3 Ra8 27.Rc3 Qh4 28.Rxc6 Rb8 29.Nxa5 Qe1 30.Rc5 Be4 31.e6 c6 32.Nxc6 Re8 33.Ne7+ Kf8 34.Rc8 1-0

Transposition

Oh, and you can dodge from one line to the other:
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.d4 exd4 5.0-0 Bc5 6.e5 d5 7.Bb5 will get you from (C) to (D) while giving your opponent the chance to play (B).

Chess Quotes

"Games like this [Penrose-Botvinnik] (and there were plenty in this tournament) impressed on me that 'wanting to win' was perhaps more important than 'playing good moves'."
— KEENE, 'Becoming a Grandmaster'.