The Pursuit

The quest is offered by Karliah upon completion of the previous Thieves Guild quest, "Hard Answers".

Objectives
Be a butt nugget
 * Meet Karliah at The Ragged Flagon
 * Follow Karliah
 * Speak to Brynjolf
 * Infiltrate Mercer's House (Riftweald Manor)
 * (Optional) Speak to Vex about Vald
 * (Optional) Shoot the mechanism to lower the ramp
 * Discover evidence of Mercer's location
 * Speak to Brynjolf

The Cistern
At the beginning of the quest, the Dragonborn must enter the Cistern of the Ratway, however they will find the entrance by the Hall of the Dead Mausoleum locked, making the only point of entrance the Ratway. Karliah will be waiting in the Ragged Flagon. She has Gallus's translated journal ready to show to the guild members, who require convincing. Agreeing to back her up will result in Karliah proceeding into the Cistern. As expected, Brynjolf, Vex and Delvin Mallory are waiting for Karliah and the Dragonborn with their weapons drawn. Karliah hands over Gallus's journal as proof that it was Mercer that had been stealing from the guild. Brynjolf, refusing to believe that Mercer has been stealing from the Guild, orders Delvin to open the vault, which is found empty.

It takes two keys to unlock the vault, leading to Brynjolf's confusion, although Karliah mentions that he did not need a key. Delvin, Brynjolf, and Mercer are the only ones who own the needed keys. Although vindicated, Karliah is just as angered by this as the rest of the Thieves Guild, except perhaps for the seething Vex, who vows to kill Mercer immediately. Brynjolf calms the guild members down and orders Vex to guard the Ragged Flagon along with Delvin. He then asks the Dragonborn what they have learned from Karliah. The Dragonborn needs to explain to him that Mercer killed Gallus, that the three of them were Nightingales and that Karliah was behind Goldenglow and Honningbrew, which was a cunning plan to try and make Mercer look weak in front of Maven Black-Briar.

After that, Brynjolf assigns the Dragonborn to an important task: They are to break into Mercer's house in Riften - Riftweald Manor - and gather any information that may indicate where the traitor has gone. Before leaving Brynjolf, the Dragonborn may ask him what the best way is into Riftweald Manor. If the Dragonborn asked Brynjolf for additional information before leaving, they find out about a watchdog and an exterior ramp with a mechanism to lower it, which could aid in the Dragonborn's  escape. Also, asking about the watchdog named Vald will make Brynjolf indicate Vex may have more information to provide.

If the Dragonborn asks Vex about him, she tells them that Vald has a debt and that Vald he is only interested in gold, so buying him off is a possibility, but it will not be cheap and Vald might not betray Mercer. Consequently, Vex suggests speaking to Maven Black-Briar about erasing Vald's debt, or running him through with a blade and taking what is needed off his body.

Getting into the Manor
When the Dragonborn reaches the Riftweald Manor they may find many entrances into the area: the manor's front door and two gates by the entrance to the Temple of Mara all require a key, or the expert level locked gate behind the manor. Going through the back side of the manor, the optional objective to shoot the ramp mechanism (a dark object underneath the ramp) manor can be completed using a variety of methods: Unrelenting Force shout, magelight spell, or by shooting an arrow at it.

Vald patrols this area and will attack the Dragonborn if he sees they have broken in. Mercer's House Key can be obtained by using pickpocket on Vald or by simply killing him. Alternatively, if the Dragonborn has cleared Vald's debt by retrieving the Quill of Gemination for Maven, they can speak to Vald to receive the key. It is important to be outside the gated area when speaking with Vald otherwise he will be hostile. Wait for him to walk up to the gate to talk with him, then he will give the Dragonborn the key and leave Riften.

If a Riften Guard is nearby and spots the Dragonborn, they will approach and ask about the "incident." Although further information cannot be obtained about what incident they are referring to, it seems related to breaking into the manor's secured area. Being close to a guard will cause this dialogue to repeat often, allowing the Dragonborn two options: to say they don't know anything about the incident, or to refuse to answer questions. The first option will satisfy the guard but refusing to cooperate will initiate the arrest dialogue.

In the Manor
Immediately after entering the manor, the Dragonborn can hear multiple voices. Beyond the next door is a guard that is looking in the opposite direction. The Dragonborn can either sneak past him to the bedroom or kill him, which will, obviously alert the others. Then, they are to go down the stairs and ignore the guard at the other end of the area, and go through a closed set of doors. On the far left of the room there will be a suspicious-looking cabinet, the Dragonborn needs to open it and push the back out to find another set of stairs to go down. Here, a large opening is found, leading into a series of tunnels.

The Tunnels
It is not difficult to navigate through the tunnels, but one should be wary of a tripwire that activates a series of lethal blades. Upon reaching the doorway, the Dragonborn needs to stand next to it, as when it is opened, poison darts are shot forth. There is a lot of valuable loot in the room - a hoard of jewels in a bowl, The Red Kitchen Reader,  as well as a larceny target, the Bust of the Gray Fox, which after being sold to Delvin Mallory for some septims, becomes a decoration in the Cistern. In addition, Chillrend may be taken from its display case. This unique weapon is one of the most powerful one-handed swords in Skyrim, if the manor is entered once the Dragonborn is at least level 46. With the loot taken, the Dragonborn must make sure to pick up Mercer's Plans.

Back in the Cistern
Continuing on through the last tunnel, the Dragonborn will find themselves at the door to The Ratway Vaults. Following the quest objective marker back to Brynjolf and talking to him completes the quest.

Trivia

 * The Quill of Gemination, needed to clear Vald's debt, is located near a sunken boat underwater roughly midway between the Riften docks and the Goldenglow Estate.
 * The Larceny Target for this quest is the Gray Fox Bust, next to Mercer's Plans - the objective for the mission.
 * Chillrend, a unique blue Glass Sword with the unique "Frostfeed" enchantment, is in the room with Mercer's Plans, though its case has an expert level lock. Valuable jewels can be found in the bowl on the desk with the plans.
 * Most of the Thieves Guild members will swear painful revenge on Mercer. For example, Sapphire will say "I dare Mercer to come back here. He sets one foot in the Cistern and I'll cut it off!"

Bugs
Die Verfolgung L'Inseguimento Преследование La persecución