- For a sub-skill of Alchemy, see Transmute.
"The Schools of Arcane Magic - Transmutation" is a book in Dalaran which is related to the 
[Higher Learning] achievement. Drunken Dalaran mages often leave it in the empty bookshelf[50.3, 40.7] near the west entrance of the Legerdemain Lounge.
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<Penned by the skilled hand of Archmage Ansirem Runeweaver>
The ninth and final school of magic is transmutation. It is among the most popular and useful of all of the schools, allowing a mage to manipulate time and space. Perhaps the most iconic Transmutation spell is 
[Polymorph], which allows a mage to turn something - or someone - into something else. Fortunately for many of my students, the effects are not permanent. I've seen more than one unwary apprentice turned into a sheep, pig, or worse - don't even ask what "worse" means.
The second most famous use for transmutation magic is teleportation. The most basic teleportation spell is 
[Blink], and it remains among the most useful. Blink can be used to quickly escape a foe - or save a mage who has accidentally fallen off a cliff. Do not attempt to use blink to escape falling to your death unless absolutely necessary. This is the kind of trick you can only fail once.
Make absolutely certain you know your destination before attempting to teleport. There's a reason we have very specific spells to teleport to certain locations - attempts to cast a teleportation "on the fly" often result in one very dead mage inside a wall, chair, or another mage. And I don't mean in a fun way.
Spells that manipulate time also fall into this category. The ever-popular 
[Slow Fall] spell is an excellent alternative to falling to your death (and much more reliable than Blink at this function). More advanced practitioners of the arcane arts can also learn a spell that slows the movements of their enemies. I've heard rumors of a spell that increases movement speed as well, but I've never seen it in practice.
Lady Jaina Proudmoore is a skilled practitioner of transmutation magic. She has developed a powerful variation of the popular mass-teleport spell that is capable of moving a significant percentage of her army with minimal effort. This spell helps make her extremely unpredictable on the battlefield.