Giuoco Piano / Two Knights Defense / Fried Liver Attack [FEN ""]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 d5 5. exd5 Nxd5 6. Nxf7 Kxf7 7. Qf3+ Ke6 8. Nc3 Ncb4


White can play 9. Qe4 (Old variation protecting c2 square from ... Nxc2+ forking King and Rook and also with attack of d4 etc.

White can also play 9. a3 allowing 9... Nxc2+ 10. Kd1 Nxa1 allowing Black to attack the Rook. Further White will play strong attacking moves like 11. Nxd5 etc. and continue the strong attack.


Is 5... Nxd5 correct or he should go to main line of Two Knights Defense with 5... Na5?
After 5... Nxd5, can White continue with 6. Nxf7 for strong attack?
After 7. Qf3+, can Black continue with 7... Ke6 challenging White in further game? Hence can we play 7... Ke6 in tournaments and continue our attack and study of opening variations?
Between 9. Qe4 and 9. a3, which variation is better for White?
Most people agree that the Fried Liver attack is better for white. So black's 5...Nxd5 is inferior to the less scary 5... Na5. Assuming that black goes in for the Fried liver though, white can play either 6. Nxf7 or 6. d4. Both lead to similar attacks. 

In the Nxd5 Nxf7 line, however, black's moves are forced until move 8, where black has the choice to defend the pinned knight with Ne7 or Nb4. Any other moves just admit defeat and give back the piece to white for a completely misplaced king and underdeveloped position.

Most pros play 9. 0-0 or 9. a3. Interestingly, Qe4 is recommended by my engine... but the a3 lines are so good for white, that I don't really see any reason to deviate. Personally, I've only played a3 with good success.