Dragon Age: Inquisition created by BioWare.
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Lotus and Root

Trigger: Speak to Mother Giselle
Reward: +1 Power, +50 Influence

This quest only triggers after you've met Mother Giselle in the Hinterlands, after which point she takes up residence in Haven. Speak to her in the Chantry's main hall and ask her what you can do for her. She'll ask you to grab some items, namely five Blood Lotuses and five Elfroots. Elfroot is bloody well everywhere in the early portions of the game, but Blood Lotuses are a little rarer. I found the water's edge of the Storm Coast the best place to hunt about for Lotuses. Take these to Threnn's requisitions table for your reward.

Haven's Best and Brightest

Trigger: Speak to Adan, Threnn, or Harritt
Reward: ... nothing...?

The most basic of side quests. All you have to do is speak to three notable members of the Inquisition. Adan, the apothecary, is in a cabin to the west of the Chantry; Threnn, the quartermaster, is just outside the Chantry; Harritt, the smith, is near the training field at the front of Haven.

Know Thy Enemy

Trigger: Automatic (I think?)
Reward: Influence

Turn in an item to Minaeve. Easy enough. She's inside the Chantry, in a room on the left side of the main hall.

Mixing Potions

Trigger: Automatic (I think?)
Reward: Influence

Visit a Loadout Station. Simple as that. You'll find one in the apothecary's cabin, to the west of the Chantry.

Passing Notes

Trigger: Speak to Adan
Reward: Lyrium Potion Recipe

You can trigger this side quest by speaking to Adan, in the apothecary's cabin (west of the Chantry), and asking if he needs any help. He'll ask you to go looking for some notes. You'll find the notes to the northeast, along a side path from the training yard on Haven's lowest tier of land. Pop inside the house here and you'll receive a tutorial for finding hidden items; the notes are on a desk in the rear of the house, beside a big wheel of cheese. Return the notes to Adan for your reward.

Piece by Piece

Trigger: Speak to Harritt about improving your equipment
Reward: Improved armour

After creating armour for The Right Armour (see below), check the crates for additional pieces that you can add onto the armour. Then modify the armour at the forge to complete the quest.

Requisition for Weapons

Trigger: Speak to Threnn
Reward: Inquisition Weapons (+1 Power)

You'll find Threnn by a cluster of tents, just north of the Haven Chantry. She needs five Iron and one Logging Stand. You can find Iron in lots of places, primarily if you check out rock formations; you'll find the like on the outskirts of Haven, if you're willing to climb the snowy hill by the siege engines in the west. The Logging Stand is found amid some wood piles in a forest far to the north of Haven's walls; you can get here by following the roads north of the training grounds and slipping behind a large-ish shack. The wood pile isn't too difficult to find. Turn both in to the Requisitions table by Threnn.

The Right Armor

Trigger: Speak to Harritt about ordering armour
Reward: A new piece of armour

After chatting with Harritt for the first time, order some armour made. You can find the pieces for the Apprentice Coat by raiding the crates around his forge. Create armour and your reward is what you created.

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