Skyrim:Alteration

Alteration, one of the five schools of magic in Skyrim, affects the world around it by altering the laws of reality and manipulating it to one's own accord. Increasing this skill reduces magicka cost when casting Alteration spells. Historical information about the School of Alteration is provided in the lore article. The Alteration skill tree has a total of 10 perks, requiring a total of 14 perk points to fill.

In-game Description: The School of Alteration involves the manipulation of the physical world and its natural properties. This skill makes it easier to cast spells like Waterbreathing, magical protection, and Paralysis.

Summary
Alteration contains a range of defensive and utility effects. 
Magic Armor spells provide a magical armor protection. The perk multiplies the magnitude of the flesh spells. Each rank in the perk magnifies the armor value by a factor of 2, 2.5, and 3 respectively.
Magic Resistance; up to a passive 30% bonus is available via perks.
Spell Absorption via the Atronach perk.  This is one of only three ways to obtain spell absorption.
Utility spells like Candle/Magelight, Waterbreathing, Telekinesis, Detect Life and Detect Dead are all of general use when exploring.
Transmute allows you to turn Iron Ore into Silver Ore and Silver Ore into Gold Ore.
Paralyze is the only really offensive aspect of this School of Magic.
In some ways the protective spells in Alteration are an alternative to the Wards found in the school of Restoration.

Skill Perks
 
 
 

 
 

Spells
 
Spell List Notes
 
Mage Armor and Exceptions

Wearing any piece of apparel with the keyword   or  , including equipping such an item after a Mage Armor spell has been cast, will completely negate the armor bonus from any Mage Armor perks. However, shields do not use either of these keywords, so equipping a shield will have no effect on the bonus. There is also a small assortment of apparel items that have an armor rating but lack the relevant keywords and thus can be worn without disabling the Mage Armor effect:

Amulet of Articulation
Diadem of the Savant
Fine Armguards
General Tullius' Armor
Locket of Saint Jiub 
Miraak's Boots 
Ulfric's Bracers

Magical Effects
A list of standard alteration spells can be found on the Alteration spells page.  The following individual effects are all considered to be part of the school of Alteration (see the individual effect pages for full details on availability; the Magical Effects article also provides a summary):
 Ash Shell 
 Armor
 Detect Life
 Detect Undead
 Light
 Paralyze
 Telekinesis
 Teleport Pet 
 Transmute
 Waterbreathing

Skill Increases
Character Creation
The following races have an initial skill bonus to Alteration:
+5 bonus: Altmer, Argonian, Breton, Dunmer, Redguard

Trainers
Dravynea the Stoneweaver in Kynesgrove (Expert)
Tolfdir in the College of Winterhold (Master)

Skill Books
Breathing Water
Daughter of the Niben
The Lunar Lorkhan
Reality & Other Falsehoods
Sithis

Free Skill Boosts
+1 Alteration reward from Dravynea the Stoneweaver for completing the quest Dravynea's Frost Salts.
+1 Alteration reward (as well as +1 to all other magic skills) from Pantea Ateia (Bards College) for completing the quest Pantea's Flute.
+5 Alteration (+5 every Magic skill) by selecting "The Path of Magic" when reading the Oghma Infinium after completing the quest Discerning the Transmundane.

Gaining Skill XP
Casting higher level spells gives generally faster skill increases (Novice<Apprentice<Adept<Expert<Master).
Regenerate Magicka effects help reduce downtimes while training. 
It is possible to reduce or even completely eliminate the magicka cost of spells by stacking Fortify Alteration enchanting effects, which is very helpful for Alteration training. The Secret of Arcana  power does the same thing, but only for 30 seconds.

Casting with Enemies Nearby
Repeatedly casting high-duration Alteration spells (like Oak Flesh, Stone Flesh, Iron Flesh, or Ebony Flesh) while in a combat situation will quickly increase one's Alteration skill.
An effective method for doing so very quickly:
# Get a melee based follower and/or conjured melee atronach (Familiar, Frost Atronach, Ash Spawn, or Dremora Lord) to attack an enemy or group of enemies. The player can usually cast their alteration spell from safety during combat while the follower and/or conjured pet do actual fighting. This allows for leveling and questing at the same time. Casting a flesh spell in one hand and Bound Sword in the other will level both Alteration and Conjuration at the same time.
# Find a place with an enemy or enemies that only use melee attacks that also has a high platform or place otherwise out of reach of the enemies. Preferably, kill all but one of the enemies: Bleakwind Basin works very well for this purpose.  Alternatively, along the shore of the Sea of Ghosts, the Horkers can be made aggressive without them actually attacking, allowing one to move far enough away to use the Wait function but still close enough to train the skill. And then there's Roadside Ruins, where a Spriggan Matron will notice the player, but she cannot attack since she's trapped inside. Slaughterfish can also be exploited by getting their attention and then standing on a nearby shore to cast. 
# With both hands, continually cast the highest level Alteration armor spell. Casting the higher-level spells progresses the skill faster (Oak < Stone < Iron < Ebony), so it might be advisable to take a break part way through to go buy them once you've reached a level where the better spells are available.  Often the enemy will run far enough away from your location to allow you to use the Wait function.  If so, wait an hour to get more Magicka to keep casting the spell, or just wait until it refills itself.  The giants in Bleakwind Basin will almost assuredly run away, though, if you're standing on the rectangular pillar near their fire. Mammoths never run away from you when they can't reach you. Using this method, one can go from 0 Alteration to 100 Alteration in roughly 40 minutes, but it depends on total Magicka available, particular spells cast, and the location chosen.
# Use a follower or permanent summon to continuously attack an NPC that cannot be killed. If your ally can keep the NPC on their knees, this leaves you free to repeatedly cast a spell.
#Once the Quiet Casting perk from the Illusion school of magic and the Throw Voice shout from Shearpoint have been acquired, one can misdirect enemies to and fro, and cast any of the "...-flesh" spells while they are searching for you. Using a magicka regeneration potion is useful in this scenario. An extra added benefit is that you can constantly sneak around enemies while casting, increasing your Sneak skill as well.
# The Paralyze spell is the perfect spell for Alteration training. If you reduce magicka cost to 0 using enchanted items, dual casting it on an enemy can level you up so fast that it might be considered game-breaking. With the Mage Stone, one can train Alteration from 15 to 100 in less than 5 minutes. It can be used to level up by making it Legendary over and over again.

Magelight
Magelight can be cast anywhere for a small amount of XP, such as while walking to some distant destination, making this a sure but slow way to level Alteration.

Water Breathing Trick
After you learn Water Breathing, another way to quickly level Alteration is to stand in water and repeatedly cast Water Breathing. You don't actually have to be underwater, just standing in it (this only applies to pools of water you could actually dive into; so the small streams in Whiterun won't work, but the river outside will, as will the pool just outside the entrance to Dragonsreach).

Casting Detect Life Spell in Cities
The Detect Life spell increases your Alteration experience depending on the number of targets it is currently detecting. Using it on your horse in the wilderness is almost useless, while using it in crowded location (the market in Riften during the day, for instance) gives incredible training speed. The more living objects in range, the better. Depending on the amount of NPCs within range, it should be possible to level Alteration from 15 to 100 in around 20 minutes in the following locations.

Between 8am and 5pm the markets in most walled cities can be used to power-level Alteration. Riften's, Whiterun's, and Windhelm's markets have particularly high numbers of NPCs, while standing between the market and Castle Dour in Solitude will boost the low market numbers with soldiers from the castle grounds. 

Later in the day moving to the main tavern will allow for more power-leveling. The Silver-Blood Inn (Markarth), The Bee and Barb (Riften), the Winking Skeever (Solitude), the Bannered Mare (Whiterun), and Candlehearth Hall (Windhelm) are the most populated inns in the walled cities. The Retching Netch  in Raven Rock also has high numbers.

After the Civil War is over, either the Blue Palace (Stormcloaks) or the Palace of the Kings (Imperial Army) will be packed with exiled Jarls and their most loyal allies. 

Casting Telekinesis
Holding any object in the air with Telekinesis without picking it up also gives a very high amount of experience. If the suspended object touches any NPC they will become hostile though, so be careful. If you can get a total of 100% magicka reduction cost (such as through the use of the Secret of Arcana  power), and fast travel while holding an object, the game will act as if you had kept casting for the whole duration of the travel, and level Alteration appropriately. For example, fast traveling between Riften and Markarth will increase your Alteration skill to 100, even if you start from 15.
A good way to level Alteration using Telekinesis is to put an object near the cistern entrance of the Thieves Guild. When you exit the Thieves Guild, keep the hatch closed (do not pull the chain) and drop your object. Then cast Telekinesis on it and fast travel somewhere on the map. You will level Alteration and the object remains near the Thieves Guild entrance. This way, you can Legendary Alteration and re-level it over and over without having to go and find the object that got away.

Transmuting Ore
Outside combat, you can gain a substantial amount of Alteration experience if you know the Transmute spell by using it to transmute iron ore into silver and gold ore. Even at low levels of Alteration, it should be possible to cast Transmute (an Adept level spell), although if you have been busy mining it may take a long while to turn all of your iron into gold (which you can then smith into jewelry for Smithing experience). The Transmute spell is not available from spell merchants, but the spell book is in two fixed locations in dungeons.