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1: Upon entering the Ruins, talk to the Guard for a breakdown of the situation, including the knowledge of a large military bot nearby. Walk forward to the end of the alley, peek left and you'll see it. I'd advise your Spy Drone (which will take three attacks) or stealthy use of your EMP grenades with a combination of alt-fire from your Mag Rail. There are two more templars in the area, one on the right and another on the left, which you'll want to take down as well.
2: This whole area in fact is teeming with templars. Not so many that it becomes overly difficult, but nearly around every corner you'll find one or two. I found it useful - after the initial two are taken down in the courtyard - to walk underneath the open multi-leveled ruins, look up and take down the couple you can see walking the beams and hiding on the floors above. While you're here, you may encounter another Templar or two that runs out from one of the doors to confront you. Enter the NW door and pick up the items under the stairs (taking out any Templar resistance), and climb the several stairways to the top.
3: Open the door and head across the level to the "Keep Out" door, confronting any Templars on the way. There is another inside who may or may not come out to find you. When they're no longer a problem, enter the Keep Out room, move the boxes and use your keycode on the secret entrance to reveal... the lab's secret entrance! For now, ignore it, and enter the adjoining room with stairway leading up. Climb the stairs, open the door and take out the Templar or two you find up here, then walk around to the door on the other end. Inside is a chest holding - if you purchased one from the Omar in Trier - a Black Market Biomod Canister and an energy cell. Backtrack down to the "Keep Out" room and enter the elevator to the Black Gate Laboratory.
4: Right when you arrive off the elevator, take out the Templar Paladin roaming the hallway nearby. Beyond the red lasers is another Templar you'll see if you wait there, that you may wish to take out from afar. Across from the elevator is a room with breakable glass. Use your glass destabilizer on it and crawl through, else use your multitool on the door to the left. Inside are some items including an image of the Black Gate Teleporter on a datacube. Crawl through the vent to emerge in a low-ceiling room with a few more items, a ladder and another vent (that takes you to the same hallway but to the left of the ladder). At the top of the ladder is a Templar, so Cloak and climb up, take him out, and proceed right. Keep right until you find T. Tong's Office.
5: Enter the office, view the holocomm from Leila Nassif, read the datacube and get the Black Gate Lab doors keycode and security login for the Black Gate terminal. Be sure to grab the THREE BIOMOD CANISTERS in the locked cabinet. Nice find! By now I've fully upgraded Spy Drone, Cloak, Speed, Biotox Attack Drone and Aggressive Defense Drone, in that order. Exit the office to the left, take your first right, pass up the Black Gate Reactor and take another right, then head all the way down to the area labeled "Containment." Disable the beams with a multitool, and head on in through the door.
6: As you approach the glass, you'll speak with Her Holiness, aka Nicolette DuClare from Deus Ex, witness another of the game's story twists, and feel somewhat odd when the Illuminati Elite trooper shows up. Enter the room and continue to talk to them until they run out of things to say, then head into the west chamber to talk with the Gray. Afterward, backtrack to the elevator, keeping right this time and for a shortcut, bypassing the red beams that used to be near the elevator. Head all the way back to Trier and the SSC Office.
7: Back at the SSC, make your way upstairs to the Visitation room to talk with Chad Dumier and Nicolette DuClare, and receive a map of the Templar Compound. Exit and head to the Queequeg's Coffee Shop to collect your reward for the investigation. Now proceed to the Nine Worlds Tavern to talk with Tracer Tong, who likes to dramatize. After that, you'll want to choose a pilot. I'd suggest Ava as it doesn't cost you anything and I like her better. Meet either her or Sid atop the helipad in between Queequeg's and the Nine Worlds. Time to fly to the Templar Compound. You'll be heading back to Trier and the Black Gate Laboratory once more before you take a trip through a portal.