The next stop on Booker's journey is the Monument Island Gateway—he's getting closer to the girl, now, and to wiping away his debt. By now, you've got a pistol and a machine gun, plus vigors that let you throw fiery grenades, set fire traps, and possess machines (like turrets and, later, humans, which then fight for you until being destroyed). And from that last boss battle, you've gained the Murder of Crows vigor, which lets you send murderous black birds directly at enemies or lay a "nest trap" activated by their footsteps.
This section is characterized mainly by the Skylines, aerial tram lines that stretch between Columbia's floating neighborhoods and platforms. You traverse them using the spinning hooks mounted on Booker's left arm, and despite how complicated it may look, the controls are actually simple. It's quite fun.
One propaganda billboard in particular stuck out to us here. It read, "Even God is entitled to a do-over, and what is Columbia but another Ark for another time?"
After solving some rudimentary puzzles, you'll finally meet the "prophet" Father Comstock for the first time.