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Skyrim:Flame Cloak

Flame Cloak is an adept level Destruction spell that surrounds the caster in flames, causing fire damage to any enemies within melee range and setting them on fire, dealing 30% of the immediate spell damage, scaling down quadratically over 2 seconds.

 
Effects
Flame Cloak, 8 points damage in 10 feet for 60 seconds.
Survival Mode: Resist Freezing Water

Perks
Augmented Flames, raises damage to 10 at first rank or 12 at second rank.

Notes
You can only have one Cloak spell of any kind active at a time.  Casting a second will cancel the first.
It is a 'smart' spell and does not damage NPCs or followers, unlike J'zargo's flame cloak scrolls.
Dual casting significantly increases its range (4.84 times the covered area), but does not increase damage.
The spell will continue to the end of its duration even if you sheathe your weapons.  It even operates under water, making it an effective means of dealing with Slaughterfish, since you can't use other attacks or spells while swimming.
One strategy for using this spell is to cast it and then simply run in tight circles around your enemies.  They may be unable to hit you, and the fire will slowly take them out.
The spell actually lasts 62 seconds, rather than the described 60 seconds, because of the added tapering time in which there is reduced effect.
When Survival Mode is active, the cloak allows swimming in freezing water without taking damage or suffering additional cold.
Potions of Fortify Destruction increase both range and damage.

Bugs
Holding a dual-cast of any spell (e.g. Invisibility, Rally, etc) while this spell is active causes its damage to increase for as long as the dual-cast spell is held and with no magicka cost.
Skyrim:Flaming Familiar

Conjure Flaming Familiar is an apprentice level Conjuration spell that summons a Flaming Thrall which will rush towards your enemies and explode. The Flaming Thrall appears as a fiery wolf, and uses melee attacks for the brief period before it explodes.

 
Effects
Conjure Flaming Familiar, for 6 secs
Explosion has the following effect:
Fire Damage, 50 pts in 15 ft for 3 secs

Perks
Summoner, increase range to 200 ft at first rank or 300 ft at second rank.
Conjuration Dual Casting, multiply spell cost by 2.8 (base 159.6, before reductions) in exchange for increasing the duration to 13.2 seconds, although it should kill itself well before this matters.
 
Notes
Dual-casting this spell increases its duration but not its damage or area.
Data in the Creation Kit indicates that this spell was originally intended to be a flaming draugr.  In fact, unlike the actual familiar, the flaming familiar has neither the keyword to make it a familiar nor the keyword to make it a daedra.
This also means it spawns with an Ancient Nord Sword or an Ancient Nord War Axe; it can equip this, as it has a right hand, and it may choose to do so, as it has 15 ranks in One-handed and uses the Draugr combat style, not the Familiar combat style.
The explosion does damage to friends as well as foes, including the caster, so try to be out of range when it blows. If no foes are close enough, it will seek out and explode on the caster.
The stats of the Familiar summoned are:
Skyrim:Frenzy (spell)

Frenzy is an adept level Illusion spell that causes creatures and people up to level 14 within a 15 ft radius to attack anyone in sight for 60 seconds.

Effects
Frenzy, 14 pts in 15 ft for 60 secs
Rally Secondary, 14 pts in 15 ft for 60 secs

Perks
Illusion Dual Casting, multiplies effective level by 2.2 (rounded down).
Animage, animals 8 levels higher can be affected.
The highest level enemy animals in the game (not counting leveled companions) are the mammoth, which is level 38, and the betty netch , which is level 40.  You have to dual cast to frenzy them, and either animage or rage is both necessary and sufficient - you can't do it without one and having both will not help you.  This means animage itself is generally a useless perk for Frenzy; against any animal target in the game, Rage will provide the same performance, and having both won't stack in a useful way.  The exception is if you are a vampire, which will stack with both enough to let you Frenzy a mammoth without dual casting.
Kindred Mage, people 10 levels higher can be affected.
Rage, all targets 12 levels higher can be affected
Master of the Mind, allows spell to work on undead, daedra, and automata.
Note that most of these perks will stack, so the overall effective values for the spell with perks are as follows:



Master of the Mind will not stack with Kindred Mage or Animage, which is primarily of interest when attempting to cast spells on vampires, when it will come up that Kindred Mage does not apply, even though vampires have black souls.  Death Hounds are not affected by Animage, but they are not animals to begin with; more generally, the perks will not combine when fighting people or animals raised by necromancers.

 

Notes
Unlike previous games, casting this spell on a non-hostile target in public is considered an assault, so you can't use it to easily murder someone in front of witnesses. However, if you are hidden when you cast the spell and nobody sees or hears you, you can still get away with it. Though if all of your witnesses are within the range of the spell, there may be nobody left to report it even if you are seen.
A more common use for this is to cast it on a group of enemies, so they all fight each other instead of you. Odds are you'll be left with just one last severely weakened enemy standing, which you can then mop up on your own.
Skyrim:Frost Cloak

Frost Cloak is an adept level Destruction spell that surrounds the caster in frost, causing frost damage to the health and stamina of any enemies within melee range.

 
Effects
Frost Cloak, 8 pts in 10 ft for 60 sec

Perks
Augmented Frost, raises damage to 10 at first rank or 12 at second rank.

Notes
You can only have one Cloak spell of any kind active at a time. Casting a second will cancel the first.
It is a 'smart' spell and does not damage NPCs or followers.
Dual casting significantly increases its range (4.84 times the covered area), but does not increase damage.
The spell will continue to the end of its duration even if you sheathe your weapons. It even operates underwater, making it an effective means of dealing with Slaughterfish, since you can't use other attacks or spells while swimming.
One strategy for using this spell is to cast it and then simply run in tight circles around your enemies. They may be unable to keep up and get a hit in, and the frost will slowly take them out.

Bugs
Skyrim:Frost Rune

Frost Rune is an apprentice level Destruction spell that creates a rune which will explode when enemies come near, causing frost damage to health and stamina. You can't cast it just anywhere. When you press the cast button, the crosshair will let you know if you are pointing at a valid surface within range. If it is red, then you can't cast the spell there.
 
Effects
Frost Rune, 50 pts for 1 sec

Perks
Rune Master increases range to 100 feet.

Notes
You can set off frost runes (your own or others) using any other Destruction spell from a distance.
Skyrim:Frostbite

Frostbite is a novice level Destruction spell that deals frost damage to Health and Stamina, and slows targets for 1 second.

Effects
Frostbite, 8 pts for 1 sec
Slow, 50 pts for 4 secs
Deep Freeze Paralyze, for 3 secs; if the Deep Freeze perk has been unlocked

Perks
Augmented Frost, raises damage to 10/s at first rank or 12/s at second rank

Notes
Like most Frost spells, it can be used to set off Frost Runes from a safe distance (though Ice Spike or Ice Storm may be preferable due to their greater range).
Skyrim:Fury

Fury is a novice level Illusion spell that causes a creature or person up to level 6 to attack anyone in sight for 30 seconds.

Effects
Fury, 6 pts for 30 secs
Courage Secondary, 6 pts for 30 secs

Perks
Illusion Dual Casting, multiplies effective level by 2.2 (rounded down).
Animage, animals 8 levels higher can be affected.
Kindred Mage, people 10 levels higher can be affected.
Rage, all targets 12 levels higher can be affected
Master of the Mind, allows spell to work on undead, daedra, and automata.
Note that most of these perks will stack, so the overall effective values for the spell with perks are as follows:


Master of the Mind will not stack with Kindred Mage or Animage, which is primarily of interest when attempting to cast spells on vampires, when it will come up that Kindred Mage does not apply, even though vampires have black souls.  Death Hounds are not affected by Animage, but they are not animals to begin with; more generally, the perks will not combine when fighting people or animals raised by necromancers.

 
Notes
Unlike previous games, casting this spell on a non-hostile target in public is considered an assault, so you can't use it to easily murder someone in front of witnesses. However, if you are hidden when you cast the spell and nobody sees or hears you, you can still get away with it.
Skyrim:Grand Healing

Grand Healing is an expert level Restoration spell, which will instantly restore the health of everyone near the caster by 200 points.
Effects
Restore Health Area, 200 pts in 15 ft
Restore Stamina Area, 200 pts in 15 ft; if the Respite perk is unlocked.
Restore Health, 200 pts
Restore Stamina, 200 pts; if the Respite perk is unlocked.

Perks
Regeneration, increases health (and stamina with the Respite perk) restoration to 300.

Notes
This spell will not heal enemies within range, only your allies and neutral targets.

Bugs
Skyrim:Guardian Circle

Guardian Circle is a master level Restoration spell, which will cause any undead up to level 35 who enter the circle to flee from combat for 30 seconds, and also heal the caster while inside the circle.

Effects
Guardian Circle, 35 pts for 30 secs
Restore Health, 20 pts for 2 secs

Perks
Necromage, increases duration of the turn undead effect to 90 seconds and affects undead up to level 43 (requires USKP).
Restoration Dual Casting, increases the turn undead effect duration to over 2 minutes.

Notes
The fear duration is independent from the circle's duration, i.e.: If an undead creature enters the circle after 29 seconds, it will still flee for a full 30 seconds, even though the circle itself has expired.
The circle does not move with the caster, but stays where it is when cast for 60 seconds.  There is no requirement that the caster remain within the circle to keep it going.  However, you will not receive healing unless you are in the circle.
The circle will not heal your allies or anyone else, only the caster.  Also, unlike standard healing spells, it will not heal stamina, even with the Respite perk. It will however replenish magicka if you have the Atronach perk as it counts as being "hit" by a spell from an outside source.
You can only have at most one Guardian Circle active at a time.  Casting a second will dispel the first.  However, you can cast it along with a Circle of Protection, and have both running at once.

Bugs
 
 
The book is added to Colette's inventory after the quest until the next inventory reset. This is because the game erroneously sets the completion flag for the Alteration ritual quest instead of the Restoration ritual quest, so the leveled list containing the book remains disabled.
  At any time after the Augur's test, enter the following command into the console to make the book available:  . If Tolfdir incorrectly has Mass Paralysis and you wish to get rid of it, enter:  . In either case, you may have to wait for the merchant's inventory to reset.
One possible way to prevent the bug is to run to Colette as quickly as possible once you pass the Augur's test. This can be made easier by doing the test at night so that Colette will be in her bed, memorizing the path out from The Midden Dark to the Hall of Countenance, setting the difficulty to Novice, and standing next to the Augur's door to sprint out as soon as it opens (don't stop to put on clothes or change spells).
Another option, if you can afford it, is to purchase everything (maybe just the books) from Colette before the Augur's test. This seems to correct the inventory reset to include the Guardian Circle Spell Tome.
This option was done successfully by only purchasing some Soul Gems from her.
It appears that removing your follower from your service before starting the trial may prevent the bug.
It seems that only using restoration spells during this test also works
Skyrim:Harmony

Harmony is a master level Illusion spell that causes hostile creatures and people up to level 25 within 250 ft of the caster to stop fighting for 60 seconds.

Effects
Harmony, 25 pts for 60 secs in 250 ft

Perks
Animage, animals 8 levels higher can be affected.
Kindred Mage, people 10 levels higher can be affected.
Hypnotic Gaze, all targets 8 levels higher can be affected.
Master of the Mind, allows spell to work on undead, daedra, and automata.
Note that most of these perks will stack, so the overall effective values for the spell with perks are as follows:


Master of the Mind will not stack with Kindred Mage or Animage, which is primarily of interest when attempting to cast spells on vampires, when it will come up that Kindred Mage does not apply, even though vampires have black souls.  Death Hounds are not affected by Animage, but they are not animals to begin with; more generally, the perks will not combine when fighting people or animals raised by necromancers.

 

Notes
Harmony will cause targets to "forget" that they have been pickpocketed recently.
Harmony is by far the most effective spell for leveling your Illusion skill, as it gives nearly six times the amount of experience of the next most useful leveling spell in the base game, Muffle, even against a single target, though it requires two targets to be more cost and time effective. It provides slightly better than triple the experience of Frenzy Rune , the next most useful leveling spell with expansions installed.  Since those two spells can be cast with a single hand, the comparison is not necessarily intuitive.  An exact comparison:


Remember that like Harmony, Frenzy Rune needs a target to provide any experience.
Skyrim:Heal Other

Heal Other is an adept level Restoration spell, which will instantly restore the health of the target by 75 pts.
Effects
Restore Health, 75 pts
Restore Stamina, 75 pts; if the Respite perk is unlocked.

Perks
Regeneration, increases health (and stamina with the Respite perk) restoration to 112.5.

Notes
Despite the description's claim that it will not work on undead, it does work on vampires (and notably, Necromantic Healing  and Heal Undead  do not).
Skyrim:Healing

Healing is a novice level Restoration spell, which will slowly restore the health of the caster.
Effects
Restore Health, 10 pts for 1 sec
Restore Stamina, 10 pts for 1 sec; if the Respite perk is unlocked.

Perks
Regeneration, increases health (and stamina with the Respite perk) restoration to 15/sec.

Notes
Combined with the Equilibrium spell from Alteration, this can be an easy (if slow) way to train the Restoration skill.
Comparing this to Fast Healing and Close Wounds, Healing is generally the second most efficient of the three. It is the most efficient until you have 70 magicka, when it is passed by Close Wounds, and it is the second most efficient until you have 330 magicka, when it is passed by Fast Healing. Fast Healing and Close Wounds are obviously preferable in an emergency though, since they work instantly.
Because all players start with this spell, the tome is only useful as decoration or as an item to sell to merchants.
Skyrim:Healing Hands

Healing Hands is an apprentice level Restoration spell, which will slowly restore the health of the target.
Effects
Restore Health, 10 pts/sec for 1 sec
This spell then tapers; it will continue to deal the original magnitude of the effect to the target for another 0.3 seconds after expiring.
Restore Stamina, 10 pts for 1 sec; if the Respite perk is unlocked.

Perks
Regeneration, increases health (and stamina with the Respite perk) restoration to 15/sec.

Bugs
Skyrim:Hysteria

Hysteria is a master level Illusion spell that causes creatures and people up to level 25 within 250 ft of the caster to flee from combat for 60 seconds.

Effects
Hysteria, 25 pts in 250 ft for 60 secs

Perks
Animage, animals 8 levels higher can be affected.
Kindred Mage, people 10 levels higher can be affected.
Aspect of Terror, all targets 10 levels higher can be affected
Master of the Mind, allows spell to work on undead, daedra, and automata.
Note that most of these perks will stack, so the overall effective values for the spell with perks are as follows:


Master of the Mind will not stack with Kindred Mage or Animage, which is primarily of interest when attempting to cast spells on vampires, when it will come up that Kindred Mage does not apply, even though vampires have black souls.  Death Hounds are not affected by Animage, but they are not animals to begin with; more generally, the perks will not combine when fighting people or animals raised by necromancers.
Skyrim:Ice Spike

Ice Spike is an apprentice level Destruction spell that deals frost damage to health and stamina, and slows targets' movement for 3 seconds.

Effects
Ice Spike, 25 pts
Perk Impact Stagger, 0.25 pts; if the Impact perk has been unlocked
Slow, 50 pts for 3 secs
Deep Freeze Paralyze, for 3 secs; if the Deep Freeze perk has been unlocked

Perks
Augmented Frost, raises damage to 31.25 at first rank or 37.5 at second rank

Notes
Like most Frost spells, it can be used to set off Frost Runes from a safe distance.
Ice Spikes which hit enemies will continue to exist after they die until you leave the area. This makes the corpses easy to spot from a distance for looting.
Skyrim:Icy Spear

Icy Spear is an expert level Destruction spell that deals frost damage to health and stamina, and slows targets' movement for 3 seconds.

Effects
Icy Spear, 60 pts
Perk Impact Stagger, 0.25 pts; if the Impact perk has been unlocked
Slow, 50 pts for 3 secs
Deep Freeze Paralyze, for 3 secs; if the Deep Freeze perk has been unlocked

Perks
Augmented Frost, raises damage to 75 at first rank or 90 at second rank

Notes
Icy Spear is essentially just a much more powerful (and expensive) version of Ice Spike.
Like most Frost spells, it can be used to set off Frost Runes from a safe distance.
Icy Spears which hit enemies will continue to exist after they die until you leave the area. This makes the corpses easy to spot from a distance for looting.
Skyrim:Incinerate

Incinerate is an expert level Destruction spell that deals fire damage and sets targets on fire, dealing 30% of the immediate spell damage and scaling down quadratically over 1 second.

Effects
Incinerate, 60 pts
Perk Impact Stagger, 0.25 pts; if the Impact perk has been unlocked
Intense Flames Fear, 99 pts for 15 secs; if the Intense Flames perk has been unlocked

Perks
Augmented Flames, raises damage to 75 at first rank or 90 at second rank
Aspect of Terror, raises damage by 10 pts (15 if both ranks of Augmented Flames are unlocked first).

Notes
Incinerate is essentially just a much more powerful (and expensive) version of Firebolt.
Like most Fire spells, it can be used to set off Fire Runes or Oil Slicks from a safe distance.
Incinerate has blank explosion. Casting the spell near guards and NPC may incur bounty.

Bugs
Skyrim:Invisibility (spell)

Invisibility is an expert level Illusion spell that causes the caster to become invisible for 30 seconds.

Effects
Invisibility, for 30 secs

Perks
Illusion Dual Casting, multiplies duration by 2.2 (rounded down)
Skyrim:Lightning Bolt

Lightning Bolt is an apprentice level Destruction spell that deals shock damage to Health and Magicka.

Effects
Lightning Bolt, 25 pts
Perk Impact Stagger, 0.25 pts; if the Impact perk has been unlocked
Disintegrate, 200 pts for 1 sec; if the Disintegrate perk has been unlocked

Perks
Augmented Shock, raises damage to 31.25 at first rank or 37.5 at second rank

Notes
Like most Lightning spells, it can be used to set off Lightning Runes from a safe distance.
Has much shorter range than the equivalent Firebolt and Ice Spike spells, but the fact that it is cast instantly instead of as a projectile makes it much easier to hit moving targets so long as they're within range.
The bolt seems to weave through its trajectory, so sometimes it misses the point of aim especially at a distance.
Skyrim:Lightning Cloak

Lightning Cloak is an adept level Destruction spell that surrounds the caster in shock, causing shock damage to the health and magicka of any enemies within melee range.

 
Effects
Shock Cloak, 8 pts in 10 ft for 60+5 sec

Perks
Augmented Shock, raises damage to 10 at first rank or 12 at second rank.

Notes
You can only have one Cloak spell of any kind active at a time. Casting a second will cancel the first.
It is a 'smart' spell and does not damage NPCs or followers.
Dual casting significantly increases its range (4.84 times the covered area), but does not increase damage.
The spell will continue to the end of its duration even if you sheathe your weapons. It even operates under water, making it an effective means of dealing with slaughterfish, since you can't use other attacks or spells while swimming.
One strategy for using this spell is to cast it and then simply run in tight circles around your enemies.  They may be unable to keep up and get a hit in, and the lightning will slowly take them out.  This is particularly effective against spellcasters, as it will also deplete their magicka.
With the Disintegrate perk, an active Lightning Cloak will instantly kill any nearby enemies who fall below 15% HP.

Bugs
Holding a dual-cast of any spell (e.g. Invisibility, Rally, etc) while this spell is active causes its damage to increase for as long as the dual-cast spell is held and with no magicka cost.
Skyrim:Lightning Rune

Lightning Rune is an apprentice level Destruction spell that creates a rune which will explode when enemies come near, causing shock damage to health and magicka. You can't cast it just anywhere. When you press the cast button, the cross-hair will let you know if you are pointing at a valid surface within range. If it is red, then you can't cast the spell there.
 
Effects
Lightning Rune, 50 pts for 1 sec

Perks
Rune Master increases range to 100 feet.

Notes
You can set off lightning runes (your own or others) using any other Destruction spell from a distance.
Skyrim:Lightning Storm

Lightning Storm is a master level destruction spell that deals massive shock damage to Health and Magicka.

Effects
Lightning Storm, 75 pts for 1 sec
Disintegrate, 200 pts for 1 sec; regardless of whether or not the Disintegrate perk has been unlocked

Perks
Augmented Shock, raises damage to 93.75/s at first rank or 112.5/s at second rank

Notes
This is the only spell in the game that uses concentration-style casting with both hands.  You still have the 3-second delay before initially casting, as with most Master spells, but once it's going, you can keep it up until you run out of magicka.
The spell only affects one target at a time, but you can keep it going by aiming it at other targets after the first is vaporized.  This may be preferable to stopping and casting again, which will require you to wait for 3 seconds for it to warm up every time.
Due to the fact that this spell cannot be dual-cast, its damage per second is significantly lower than most expert level spells. However, its damage per magicka efficiency is one of the best in the game. 
This spell has the longest range of any focus spell in the game. It is easily capable of hitting flying dragons, and this coupled with its instant speed makes it one of the best anti-air spells in the game.
Like most Lightning spells, it can be used to set off Lightning Runes from a safe distance, though it's quite overpowered and not cost-effective for that purpose.
Oddly, Lightning Storm does not kill hawks.
There is a Master level fiery version of this spell, named "Dragon Breath", which is only available through console commands.

Bugs