Skyrim:Fire Damage

Fire Damage is one of the three elemental types of damage available from the School of Destruction, the other two being Frost and Shock Damage. Fire damage has the unique ability to set its target on fire for several seconds, causing additional damage through burning (usually ~10% of the immediate damage). The environment can also be set alight which will also cause damage to enemies that pass through the flames, although the effect only lasts for a very short duration.
Fire Damage's primary advantage is that it is the strongest element in terms of damage (both direct and over time), and that there are a fair amount of foes in Skyrim that are either non-resistant or outright vulnerable to fire (Nords, draugr, spriggans, just to name a few). On top of that, Fire Damage's AoE spell, Fireball, has the longest range of any of the element's AoE spells.  Finally, Fire damage is also the only element that can trigger oil traps without the help of a lantern jug. Its primary disadvantage however lies in a questionably useful master spell, and the fact that those enemies that are resistant to fire are unfortunately the most common in their category (Fire Atronachs, Fire Dragons, etc), especially on Solstheim.

There are more variants of the Fire Damage effect than of any other effect in the game, with 70 distinct magical effects that produce fire in some form or another. This allows the game to use different visual effects for various types of fire damage, and also is one way that side-effects of the fire are customized. Other side-effects of fire spells are implemented by including multiple effects into a single spell.

Enchanting
The following items use this effect.  You can learn how to enchant custom items with Fire Damage if you find one of the following items and disenchant it:
All weapons of Embers
All weapons of Burning
All weapons of Scorching
All weapons of Fire
All weapons of Flames
All weapons of the Blaze
All weapons of the Inferno
Steel Battleaxe of Fiery Souls
Herebane's Courage
Artifacts and unique items that use the effect but cannot be disenchanted include:
Red Eagle's Fury
Goldbrand 
All Torches
Items that inflict Fire Damage but use a different variant of the magical effect include:
Dawnbreaker
Trollsbane
J'zargo's Flame Cloak Scroll
Staves that inflict Fire Damage but use a different variant of the magical effect include:
Staff of Incineration (Incinerate)
Dragon Priest Staff (Fire Barrier)
Staff of Hag's Wrath (Fire Barrier)
Staff of the Flame Wall (Fire Barrier)
Eye of Melka (Fireball)
Staff of Fireballs (Fireball)
Forsworn Staff (Flames)
Staff of Flames (Flames)
Staff of Firebolts (Firebolt)

Artifacts that increase the Fire Damage effect on spells, weapons and shouts include:
Ahzidal 

Spells
The following spells use the Fire Damage group of effects. Following each spell is the specific variant of the effect that it uses, as well as how much it burns the target for, and for how long (fire damage spells employ tapering, meaning the burning damage is not constant; the listed magnitude is how large the initial burn is):


Note that, with the sole exception of Ignite, all of the above spells taper quadratically (taper curve 2); Ignite tapers off linearly (taper curve 1).  As with all taper spells, tapering does not begin until the spell itself ends, which is primarily an issue with Flame Cloak, Flames, Ignite, and Wall of Flames.

Also, there is a spell that is not acquirable in game:

Firebolt Storm
Firebolt Storm Spell ( ;  )
Firebolt Storm Spell ( ;  )

Notes
All characters start off with the spell Flames, regardless of race or gender.
The perk Augmented Flames increases the damage done by all Fire Damage spells.
The perk Intense Flames causes the Fear effect Intense Flames Fear'' to be added to all Fire Damage spells.
While a weapon with a Fire Damage enchantment is drawn, NPCs may comment as if you're using a fire spell.
Running into water will not stop fire damage.
Fire damage can also be caused by touching lava , doing this will cause 150 pts of fire damage as well as 15 pts of fire damage for four seconds.
Fire damage enchantments are reinforced by both the "fire enchanter" (from the enchanting skill-tree) and "augmented flames" (from the destruction skill-tree) perks. 

See Also
This effect is related to:
Weakness to Fire and Resist Fire
Damage Health, Frost Damage, Shock Damage