Objective 1: Go to Andrew Ryan’s OfficeAndrew Ryan is the key to getting out of Rapture. He’s holed up in his office, here in Hephaestus. 
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Exit the Bathysphere Station and proceed left around the circular glass-enclosed corridor towards Ryan’s office. A pair of Thuggish and Houdini Splicers attack—use the Electro Bolt 2 and Shotgun to dispense with them and continue on your way. Descend the slope past the machinery and enter the room to the east.
Continue south into the next room and take the Grenade Launcher off the desk in the center. Search the desk and stand in the area for a Heat-Seeking RPG to fall from the delivery tube overhead. A pair of Spider-Splicers follow soon after, so have the Machine Gun ready to fire.
Destroy the Security Camera over the door leading to Ryan’s office and pay a visit to the U-Invent machine to the right. You probably have dozens of components that you can use, so go ahead and load up on Heat-Seeking RPGs, Exploding Buck, and Antipersonnel Pistol Rounds.