With 4.Bc4, White directly defends against Black's threat of 4...g4; White vacates the f1 square for their king once they are checked by the Black queen on h4.

From here, Black has two main options; continue with 4...Bg7 development, or push forward with their plans with 4...g4 to unseat the f3 knight. After the latter, there are many great aggressive options for White.

• The most popular continuation is the Muzio Gambit with 5.O-O, giving up the f3 knight but establishing a monstrous lead in development, with which White will mercilessly attack Black.
• Another fun option is the Lolli Gambit with 5.Bxf7+, sacrificing the bishop on f7 but luring Black's king out into the open, giving rise to another ripe attacking position for White.
• A more mainline option is the simple 5.Ne5, the Salvio Gambit; after 5...Qh4+, we see the deeper point behind the earlier 4.Bc4; White can now play Kf1 (similar to the King's Bishop Gambit). White pursues an attack against Black, down only a pawn instead of a piece.

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1.e4 e5 2.f4 exf4 3.Nf3 g5 4.Bc4

Wikipedia has related information at Kings Gambit.

• Modern Chess Openings: MCO-14. 1999. Nick de Firmian, Walter Korn. ISBN 0-8129-3084-3.