Name Reward
The leathersmith's request 200en
A local leathersmith has requested a group of explorers to retrieve 3 Long Pins for him.
Fight Hedgehog in the 1st Floor. They drop the Long Pins with a 50% chance, if you kill them in one turn.
Pure mineral water Freeze Oil
A local restauranteur needs his supply of clear mineral water replenished. Retrieve some from the Labyrinth.
In the 1st Floor, make your way to the upper right corner of D3. Examine the Wet Rock.
The item trade I Wood Bow
Sitoth Trading is developing a new weapon, and they need explorers to collect the materials for it.
Requires: 1 Bug Wing and 1 Bent Twig. The Bug Wing can be collected from the Venomfly. The Bent Twig can either be chopped in the 3rd Floor or is dropped from the Fangleaf. Note that Fangleafes are in the 2nd stratum.
A cranky monster Nectar
A monster resting in the 1st floor woke up and began to attack the passersby! It must be defeated.
Go to B2 in the 1st Floor. Defeat the FOE named Gashtor.
In the Duke's service I Power Ring
The Grand Duchy seeks a guild that can spare a landsknecht who has reached at least level 3.
Level up a landsknecht in your party to level 3+. 
Supply lines Fire Jar
We require an able guild to deliver supplies to a group of guards in the Labyrinth. Apply immediately.
Your team must get to the 4th Floor (and back) without dying. FOEs on 2nd and 3rd Floor can be avoided, if you are careful. Stay away from C1 in the 3rd Floor at this point.
Sounding the call Poison Gas
The Grand Duchy's guards are looking for 3 Red Shards to fashion their traditional hunting horn.
Fight Redhorn to get Red Shards. Can be found at E3 in the 3rd Floor (and beyond).
The item trade II Pure Vest
Sitoth Trading has another request for materials used in a new armor.  Go and find the items they require.
Required: 1 Metal Hull and 5 Bug Shells. Kill Kingmai for the Metal Hull and Ladybug for the Bug Shells, afterwards sell those materials at Sitoth Trading to complete the quest. 
In the Duke's service II Charm Gas
The Grand Duchy seeks a guild that can spare a protector who has reached at least level 3.
Level up a protector in your party to level 3+.
The nameless flower 400en
Bring an old lady her proposal flower in memoriam of her late husband.
Just go to the 5th floor D6 is where the navy flower is located

Special projects team

Life Belt
The 4th floor monsters are becoming more aggressive. Stay there for three days, slaying as many as possible.
Your quest is to survive for three days on the 4th floor; it's harder than it sounds for most groups. Just find yourself a safe spot to run up and down and fight the encounters until its over. Every day, a message will pop up and tell you how many days you still have to fight.

Your best bet may be to go down there before hand, kill the Raptor in the hidden area (entrance is at C6) and then use it to wander in as it has a lower encounter rate and, if I recall, you cannot encounter a single Evil Eye there (which blindsides 100% of the time).

The choice of how to do this is yours: A medic is helpful, but you can also bring a bunch of Medica to fight your way through as I did. You can always use the XP! Another choice is to use Ward Chimes to lower the encounter rate to pass more time.

Doing the quest at a later point is fine aswell: You still get a nice chunk of XP and items and the quest itself is much easier.

The dying forest Volt Jar
The Labyrinth's trees are dying of an unknown disease. Please help us investugate the phenomenon.
Go to the hospital at night to start this quest. Afterwards go to three locations in the labyrinth, where trees turned to stone. The locations are: Floor 4, A5; Floor 5, A1; Floor 6, B7.
Paint the town blue Blind Gas
The Amazonite used to decorate the town's roads is old and worn. Bring 5 new rocks to replace it.
You just need to get 5 pieces of Amazonite. Either mine the Amazonite at mining points on the 1st Stratum or kill Mystue in the 2nd Stratum until you have 5 pieces.
Braggart Chap's tall tale Fungus Jet
Another of Braggart Chap's stories talk of a pond that holds the moon's tears. Right...
Go to Floor 5, B4 at night. You will find a small pond and get Moon Tears to finish the quest.
Medicinal research Medica II
New medical experiments are underway at the hospital. We ask that you assist them in gathering ingredients.
This quest is easy: Get yourself a Mint Leaf from gathering points in the 2nd Stratum or kill Moriyana until they drop one.
Volunteer service I Amrita
The hospital lacks trained medics to deal with those wounded in the recent shipwreck. Please send help.
Level up a medic in your party to level 12+.
Connoisseur of leather Warp Stone
Lord Gascoyne collects animal hides, and greatly desires the skin from a rare Labyrinth denizen.
Go to the 6th floor. Just move down on the map to trigger the event that spwans the Fleehog. It starts running away from you, moving towards the gathering point on the map. Just can just catch it normally or use a Sleep Bell if you want to, but once the battle starts, this quest is basically over, since you get a preemtive strike. Slay the monster and finish the quest.
Uncharted territory 1,000en
We would like to increase security on the 7th and 8th floors, but we need more details on their layout.
To finish this quest, you obviously have to map the 7th and 8th floor, but the trigger for the quest is kinda weird, so there's no real way to know if you finished a floor or not. I actually started the quest after killing the Hellion, so I already had a finished map. I just went from floor 6 to floor 8 on the normal way and afterwards entered floor 7 and 8 again to unlock it.
Labyrinth stew Metopon
The Labyrinth Lunch is a popular meal, but we're out of ingredients
Required: 1 Moving Eye, 3 Mugwort. Fangleaf drops the Moving Eye and Mugwort can be farmed at gathering points (take) in the 2nd Stratum, for example in the 6th floor.
That ephemeral flavor Stonard
I need a fruit from the forest, but it starts to go bad right away. Bring it back immediately!
Go to the Flaus Inn. The innkeeper will tell you, that you need to acquire some fruit for a VIP. So go to the 8th floor and pick up a Strawberry at the gathering point. Afterwards, go to Floor 4, D5 and a scene with a guard will trigger.
Smithy Thompson's request I Fungus Jet
Thompson at Sitoth Trading needs certain materials to complete his latest project.
Required: 1 Fluorite and 1 Open Cap. Flourite can be mined in the 2nd Stratum. Also Nastue drop it. Open Caps can be obtained from Bigcap.
Man down Flame Jar (+ 300en - 600 en)
A guild has lost one of its number. To claim revenge, they need an alchemist to help defeat the monster.
You need an alchemist to finsh this quest; Level 2 should be enough to finish it and get a bonus of 300en. It seems like the 600en bonus is unlocked, if your alchemist knows flame. You always get a Flame Jar, regardless of Level and Skills of your alchemist.
A long way down Beast Bell
Lord Gascoyne discovered a threat to Lagaard while in the Labyrinth. Someone must put a stop to this!
The quest states that the monsters can be encountered in the 10th floor, but you can actually find them in the 8th floor; the quest immediately triggers, when you enter the floor. You have to fight 3 Spectre, FOEs that are unique to this quest.
Toward a cozier inn Sleep Gas
Another request from the Flaus Inn, this time to collect materials for their upcoming renovation.
Required: 2 Red Root and 3 Hardwood. Both items are obtainable in the 7th Floor at the chopping point.
Many happy returns 300en - 1,500en
We'd like to give the Duke's daughter jewelry for her birthday. Can you find us some precious stones?
In this quest, every floor from 1 to 10 has one extraction point where you can find gemstones. Some of the points only have normal stone, which are useless for jewelry, while some have gemstones which will increase the reward for every one you find. Here's the list for all the points:

1st Floor, A2: Stone; 2nd Floor, C1: Stone; 3rd Floor, C4: Gemstone; 4th Floor, A4: Gemstone; 5th Floor, B1: Stone; 6th Floor, C3: Gemstone; 7th Floor, C4: Gemstone; 8th Floor, E7: Gemstone; 9th Floor, A4: Stone; 10th Floor, D1: Gemstone

Volunteer service II Therica AX
The influx of wounded Labyrinth explorers has depleted our supplies. We need ingredients for the medicine.
Requires: 5 Mint Leaves and 3 Beast Hides. The Mint Leaves are obtainable from gathering points (take) in the 2nd Stratum and the Beast Hides are dropped by Razeking, Redwood and Gigaboar.
To the bitter end Ice Mist
My love... My only love... I want the monster that killed him dead! I will have my revenge!
Go to the 12th floor, B05. There you will find a FOE named Killfish. Kill it and the quest is finished.
In the Duke's service III Haste Pin
The Grand Duchy seeks a guild that can spare a survivalist who has reached at least level 3.
Level up a survivalist to level 3.
The naturalists 2,500en
We need more details about the monsters in the Labyrinth. Log over 50 entries in the Monstrous Codex.
This quest is easy. If you took your time to explore the floors, you should have 50 entries already. just go to the palace, use the talk option and return to the bar to finish.
Playing Cupid I Fate Beads
No matter what I give this girl, she won't warm up to me. Please find something she can't say no to!
Mine an Ice Sheet in the 12th floor and bring it to the bar.
Under maintenance Soma
We need rocks from the Labyrinth quarries for town maintenance. Help us carry them back to Lagaard.
Get the rocks from miners at Floor 3, D2, Floor 5, A3 and Floor 14, C7. You have to bring them to the bar everything you pick one up, because you can't carry more than one rock.
Yggdrasil cider Medica III
I ran out of my best liquor... You have to help me get some more ingredients from the Labyrinth!
Requires: 2 Blue Core, 2 Death Stem, 2 White Chip. Blue Cores can be obtained from Blue Gels, Death Stem can be farmed at Chop points in the 3rd stratum and White Chips are dropped from Darksoars.
The company performer Axcela
The naval band is hiring a troubador to support the front lines.
Get yourself a Troubadour.
Just out of reach Medica IV
I found a hole on the 13th floor.  There's something good inside...Wanna check it out?
Go to Floor 13, D1. In the left upper corner of D1 is a guard, that will encourage you to grab to object in the hole. Doing so will trigger a fight against a Clawbug. Kill it to finish the quest.
Playing Cupid II 3,500en
She didn't seem to like the gift you brought me before. I need something she can't resist! Please help me!