Skyrim:The Pursuit

Quick Walkthrough
# Enter the Ragged Flagon through the Ratway.
# Meet Karliah in the Ragged Flagon.
# Speak with Brynjolf in the Ragged Flagon.
# Go to the backyard of Riftweald Manor.
# (Optional) Deal with Vald.
# Enter the house through the top door.
# Go to Mercer's office.
# Take the plans.
# Return to Brynjolf.

Detailed Walkthrough
thumb|right|You're expected in the flagon
A Thief Among Thieves
Head to the Ragged Flagon through The Ratway. Meet Karliah after entering through the door to the Ragged Flagon and follow her as she leads you to the Cistern, where Brynjolf, Delvin and Vex are waiting with knives drawn. Karliah pleads clemency and hands over the journal you translated in the previous quest as proof of her innocence. Brynjolf is shocked at the revelations contained within and determines that they must open the vault to see the truth. Follow them as they head to the vault and watch as Delvin and Brynjolf use their respective keys to open it. As soon as the doors open, Brynjolf will let out a cry of horror at seeing the place completely empty; not a single gold coin is left. While Delvin is distraught at seeing their fortune gone, Vex's reaction is more violent; she pulls her dagger out and vows to kill their treacherous Guildmaster immediately. Brynjolf manages to calm the situation and asks to talk to you after assigning the other two to keep an eye out for Mercer. Tell him everything and he'll instruct you to break into Mercer's home to look for clues. However, the place is guarded by a Nord lout named Vald who is quite insistent on keeping people out. Brynjolf suggests you speak to Vex about him, since she was at one point intimately acquainted with Vald. Vex suggests the best course of action would be to erase his debt with Maven Black-Briar or run him through and take what you need off his body. You must pass a hard-level Speech check to persuade him to give you the key.

If you don't wish to kill Vald yourself, and don't want to pay the debt, you can sneak to the back of the house and shoot the ramp contraption. Vald will become hostile and chase after you. Lead him to the marketplace or any other area with guards and they will kill Vald. Loot his body and take the key. It is also possible to climb up the exterior of the Temple of Mara, by jumping onto the braziers and from there scaling the roof. From there, you can use Whirlwind Sprint to reach the balcony without ever interacting with Vald.

A Plot Revealed
Get a good vantage of the mechanism under the ramp and attack it using a ranged weapon (magic, bows, and shouts all work). The ramp will crash down, providing access to the second floor and the rest of the house.

The first room is unguarded. The next has a single guard who should be facing the west wall, allowing you to sneak past easily. The stairs down are to the northwest. At the bottom, another guard will be patrolling.

When you reach the bottom of the stairs, immediately face east and there will be closed doors. Head through them. On the northeastern corner to the barred front door you'll see a Suspicious Cabinet. Open it and then open the false back panel. Inside is a stairway down to the cellar, which leads to an underground system of tunnels.

After avoiding the pressure plate by the metal gate that you see when you first enter the tunnels, make a left and head south towards a room filled with circle-shaped traps. Looking at the tiles, head south two squares, west two squares, north two squares, west two squares, and south two squares in order to avoid the traps.

The hallway after the trap room has a pressure plate trap right around the corner that will launch a series of darts in front of the plate. Past this trap there is a chest on the right, which was on the other side of the metal gate at the beginning.

Following the hallway, you come to a hallway filled with timed pendulum blades and battering rams. Sprinting is a useful way to get past them. Once at the other end, head down the ramp and stop at the closed door. There is a dart trap trigger on the left side of the door. On the other side of the door are, among other things, Mercer's plans, a note titled Many Thanks, a copy of the Sneak skill book The Red Kitchen Reader, and Chillrend in a case. On the desk is the Bust of the Gray Fox, which can be sold to Delvin as part of The Litany of Larceny quest. There is also a stash of jewels hidden in the bowl on Mercer's desk.

Continue along the path until you reach the entrance to the Ratway Vaults. Fall down the hole (you may be attacked by some Vagrants and Lowlifes even if you had previously cleared the Ratway) and turn right to reach the Ragged Flagon. Return to Brynjolf and hand over the plans.

Notes
 
If Vald's debt has been cleared by fetching Maven her quill and you decide to go with Brynjolf's suggestion of shooting down the ramp to the second floor, Vald becomes hostile upon seeing you for "missing" the shot.
There is a Sneak skill book on Mercer's Desk.
It is possible to scale the roof of Riftweald Manor and approach the balcony from above, negating the need to activate the ramp.
The quest marker in Riftweald Manor is not positioned at the quest target and is thus not useful here.
Vald and the Marauders will attack each other if you lure the Marauders out of the house.
Members of the Thieves Guild will have varying reactions if you attempt to talk to them before proving Karliah's innocence.
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Bugs
 
 
 
A possible solution is to go to the Flagon and move her via console commands:   to select Karliah, followed by   to move her to you. You may need to manually advance the quest as well with  .
  It is possible to re-enter the Dwemer Museum in Markarth. This will reset the previous quest; run all the way back up and get the translation off the stone in Calcelmo's tower again, and return to the inn in Winterhold. The conversation with Karliah and Enthir should now be reset. This time, when Karliah tells you to meet her at the Ragged Flagon, wait until she leaves the cellar, and then wait there for a day or so just to be sure. At this point the quest marker should appear in Riften, indicating that Karliah is now where she should be.
This bug may lead to conversation options allowing you to own more than one Nightingale Blade.
 
This bug happened because Mercer's Plans is in your inventory. Drop it and enter console command  setstage tg07 10  will start the quest normally.
 
 
Using magic to pacify him might give you a chance to get into dialogue with Vald. If successful he will also probably leave after ending the dialogue without any more hostilities.
 
 It is possible to release the ramp using the console command  
 
 
If this happens attack her a few times, and eventually she will kneel, after a recuperation period she will get up (she may be hostile, either calm her or attack her again). You may need to repeat, but eventually she will no longer be hostile and begin to walk towards Riften. Fast travel there and enter The Ragged Flagon through The Ratway as normal. By the time you get there the quest should have updated to "Speak with Brynjolf."
This bug is denoted by strange quest markers such as:(Follow Karliah being the active quest) from The Ragged Flagon to The Ratway Vaults to Riftweald Manor, however upon exiting to Riften the quest marker should be at her correct location on the world map.

Quest Stages