2 c3 [B22]
In the main line 1.e4 c5 2.c3 Nf6 3.e5 Nd5 4.Nf3 Nc6 5.Bc4 e6 6.d4 cxd4 7.cxd4 d6 8.0-0 Be7 9.Qe2 0-0 White usually plays 10.Qe4, but here Radjabov plays 10.Nc3 Nxc3 11.bxc3 dxe5 12.dxe5 Qa5! 13.a4!?:
This looks at least as good as White's other tries in this position. See Radjabov - Dominguez Perez.
Grand Prix Attack [B23]
Subscriber Michael Wurm asks about the unusual 1.e4 c5 2.Nc3 Nc6 3.f4 g6 4.Nf3 Bg7 5.a3, passing the move to Black. This is also relevant to a certain line of the English Opening!
This move should not be dangerous, but Black should be aware of the tricky 5...e6 6.d4!? see subscriber question - 5.a3 in the Grand Prix Attack.
Rossolimo 3...e6 [B30]
Radjabov's favourite 1.e4 c5 2.Nf3 Nc6 3.Bb5 e6 comes under fire from Carlsen after 4.0-0 Nge7 5.c3 a6 6.Ba4 b5 7.Bc2 Bb7 8.Qe2:
I think Black can improve with a sharp idea contained in the notes. Instead Carlsen - Radjabov saw Black on the cusp of defeat, but one last trick showed itself and White fell right into it.
Moscow Variation [B51-2]
In the Hybrid variation 1.e4 c5 2.Nf3 Nc6 3.Bb5 d6 the move 4.Bxc6 should not be underestimated. After all, 4.Bxc6 is popular after 4...g6 and 4...e6. Here White tries the sharp 6.h3 Bh5 7.e5!?:
I think if Black is up for the challenge, White risks as much as Black in this line. See Nikolenko - Inarkiev.
One of the main lines in the Hybrid is 1.e4 c5 2.Nf3 Nc6 3.Bb5 d6 4.0-0 Bd7 5.c3 Nf6 6.Re1 a6 7.Bf1 Bg4 8.d3 e6 9.Nbd2 Be7 10.h3 Bh5 11.g4 Bg6 12.Nh4 Nd7:
Another main line is 1.e4 c5 2.Nf3 d6 3.Bb5+ Nc6 4.0-0 Bd7 5.Re1 Nf6 6.c3 a6 7.Ba4. After 7...b5 (We have also covered the alternative 7...c4) 8.Bc2 e5 Black heads right for the line 9.h3 g6 10.d4 Bg7 11.dxc5 dxc5 12.a4 0-0 13.axb5 axb5 14.Rxa8 Qxa8 15.Qd6, which we have seen before, in Tiviakov - Kuzubov. This line loses a pawn for Black and thus seems rather depressing.
4. Qxd4 Sicilian [B53]
Dreev uses the Anti-4.Qxd4 move order with his 1.e4 c5 2.Nf3 d6 3.d4 Nf6, but after 4.Nc3 cxd4 White plays 5.Qxd4!? anyway in Vasiukov - Dreev. Dreev invites complications with 5...a6 6.e5 Nc6 7.Qa4 Ng4 8.exd6 Qb6, but White is not ready for the critical 9.Nd5 and blunders as soon as Black assumes the initiative.
Best wishes, David