Alchemy isn't so much a single field of study as several branches of magic that can all be put into a similar category. As a General Rule Magic of this category focuses on sending power from one source to another.
Homunculi (Eizbern)
This Field covers the creation of life, and the conversion of it, as well as the innate magic that Homunculi have access to.
Flash Air (Ainsworth)
This Field Covers the conversion of small area's of space. Mainly being able to convert matter found within that space into a different location. More commonly known as teleportation, but a bit more complicated. Also to a small extent this includes the ability to manipulate one's soul.
Metal
This most common School of Alchemy but by no means the weakest. This field covers the conversion of matter into different forms. Turning lead to gold is the least of their abilities. Generally Potions of immortality, and stones of infinite energy are the end goal for any alchemist of this field.