Thief 3 Deadly Shadows:
Arrow Shops:
Each shop only has one of the four elemental arrows. 

South Quarter (Well Equipped Thief): Water Arrows
Stone Market Proper (Marla): Moss Arrows
Docks (The Undercurrent): Fire Arrows
Old Quarter: Gas Arrows 

Free Water Arrows:
Get free water arrows in the training mission by waiting by the "douse the torch" exercise for water crystals to keep respawning. You can carry a max of 25 water arrows.

Metal Age Nightvision: 
Although shadows are important to hide Garrett, sometimes it can too dark to see while hiding. Crank up the Gamma/Brightness correction in your options menu to see the surroundings while remaining hidden. 

Don't Leave Angry: 
Since the stages are often divided up into separate maps, you find yourself transitioning from one part to the other. If you are being chased by a guard, never leave the map and come back expecting everything to be normal. The guard chasing you will still be there and alerted to your presence. Always make an effort to hide in the same map you are to avoid forgetting that a guard (or party of guards) are waiting for you on the next map. 

The map transitions are a good place to hide (they are almost always completely dark): 
Simply go into the map transition and decline to go into the next section. Garrett will stay in the murky, smoky portal and almost always out of the way of all patrols. 

Factionalism:
By day 3 (after meeting with the Keepers the first time), players may choose to ally with the Hammerites, the Pagans, or both by doing them small favours. Allies are helpful since they will not attack you, and allow you to hide in their turf when you flee the City Watch (who you may never ally with). 

Befriend the Hammerites by locating and destroying the large cockroaches that inhabit the city. For each one you destroy, you increase Hammerite friendliness by one point. You also befriend Hammerites by destroying any undead using Holy Water or Fire Arrows. This may take a little while, but the beetles are easy to find. Undead are even easier to find, but you may need to stock up on fire arrows to deal with them adequately. 

Befriend the Pagans by locating green stones with the mark of the Trickster or by locating the elemental archway in the Pagan turf and firing a moss arrow into the target. The green stones are harder to find early in the game, so the elemental arch is a much better choice to befriend the Pagans. Simply shoot any one of the four purple nodes on the arch with an elemental arrow. Consider using moss arrows for this purpose; you can fire as many elemental arrows into the Pagans' elemental arch as you can afford to immediately ally them with you when the opportunity arises. 

Moss arrows are more plentiful as you pick up many in the city; more if you don't use them. You can save your fire, gas, and water arrows for your missions. 

Final Note: Killing, blackjacking, or looting from the Hammerites or Pagans will decrease your standing with that faction. 

Item Maximums: 
Gear and items are bought to be used in Thief 3. Don't go to great lengths to save items if you think they can help you stay alive and undiscovered, but don't waste them on lone guards or civilians who cannot fight back. 

On normal, the maximum gear Garrett may carry is:
Health Potion = 10 
Broadhead arrows = 30 
Noisemakers = 5 
Water Arrows = 25 
Moss Arrows = 20 
Gas Arrows = 5 
Fire Arrows = 15 
Flash Bombs = 20 
Explosive Mine = 5 
Gas Bomb = 5 
Oil Flask = 5
If Garrett proceeds to pick up another item when he is at maximum capacity, the item is "picked up" but is not added to the inventory. Be sure you have room before you start grabbing items or you're just wasting hard earned loot!