The Pursuit

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

Objectives

 * 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

Walkthrough

 * 1) This quest begins with the first objective already in play. The Dragonborn will find that the entrance by the Hall of the Dead Mausoleum is locked, making the only point of entrance the Ratway. Karliah will be waiting in the Ragged Flagon. She has Gallus' translated journal ready to show the Guild members, who require convincing. Agree to back her up and move 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.
 * 2) Brynjolf cannot believe Mercer has been stealing from the Guild, so he 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 Guild, except perhaps for the seething Vex, who vows to kill Mercer immediately. Brynjolf calms the guild down, and orders Vex and Delvin to guard the The Ragged Flagon. Then he asks the Dragonborn what has been learned from Karliah. Explain 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. Then Brynjolf has an important task: Break into Mercer's Riften house - Riftweald Manor - and gather any information that may indicate where the traitor has gone. Before leaving Brynjolf, ask him what the best way is into Riftweald Manor. Information is received about a "watchdog" and an exterior ramp with a mechanism to lower it, which could aid in the Dragonborn's  escape. Then ask about the watchdog, named Vald. Brynjolf indicates Vex may have more information to provide. These grant two optional objectives.
 * 3) If the Dragonborn wishes to clear Vald's debt, locate Vex in the Cistern or Ragged Flagon, and ask her about him. She tells the Dragonborn that 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.
 * 4) Work around Riften until the Dragonborn is behind Riftweald Manor. There are many entrances into the area. Go through the expert level lock into the back, or there is a gate that requires a key. The Unrelenting Force Shout can be used to take down the ramp, or the trigger can be shot (hitting it with a Magelight spell also works). Hide from Vald and sneak into the manor, pickpocket Vald for the key, or kill him. Alternatively, if the Dragonborn has cleared Vald's debt by retrieving the Quill of Gemination for Maven, go through the novice level lock in the front of the manor, and then the one after that. Do not pick the expert level lock. Stand outside the gate with the expert lock and wait for Vald to approach. Talk to him, and he will leave Riften, allowing the Dragonborn to do as they please.
 * 5) Voices can be heard immediately after entering the manor. Beyond the next door is a guard that is looking in the opposite direction. Sneak around to the bedroom or behind him and kill him using a sneak attack, or try to sneak by him to the next room. Go down the stairs and ignore the guard at the other end of the area, go through a closed set of doors. On the far left of the room there will be a suspicious-looking cabinet, 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. It is not difficult to navigate, but beware of a tripwire that activates a series of lethal blades. Soon a doorway will be reached. Stand next to the doorway 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 from being sold to Delvin 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.
 * 6) Continue on through the last tunnel and the Dragonborn will find them self at the door to The Ratway Vaults. Follow the quest objective marker back to Brynjolf talk to him to complete the quest completed.

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 Mercers 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
if you have collected Mercer's plans already, the quest will not start. To fix this, reload the Hard Answers quest and drop the plans back at Riftweald Manor before completing the Hard Answers quest. The Pursuit quest will then work.

Die Verfolgung L'Inseguimento Преследование