Ars Aetherae

The Ars Aetherae are the unique magical abilities possessed by unicorns.
All unicorns possess some level of ability with magic, but not all become masters of it. Most possess a small repertoire of spells suited for daily life and that compliment their vocation, special talent, and/or their interests. Dedicated students of the arcane are capable of far more.

Training
Unicorn magic is cerebral; it is learned through academic study and pefected through rigorous practice. Young foals learn the basics from their parents or private tutors, while older children typically receive additional training while in school. Those who desire to specialize and pursue advanced studies in magic enroll in various universities and schools dedicated to that purpose, the most prestigious of which is the Imperial School for Gifted Unicorns.

Mechanics
A unicorn's casting of a spell relies on three factors: a spell matrix, magical power, and manifestation.
A spell matrix is the pattern or underlying structure of a spell itself. Typically, spell matrices are recorded using an elaborate system of glyphs and symbols that pictorially represent the manner in which the spell operates. A trained unicorn can interpret the written form of the spell matrix and recreate it within their mind.
Once a spell matrix exists in the mind of a unicorn, power must be applied to it. Unicorns can draw on their innate magical reserves as well as external sources to fuel their magic.
Lastly, the power flows through the spell matrix and activates it. Once the spell matrix is active, it is released and projected through a conscious application of the will. The power then flows out of the unicorn's body and manfiests the intended result, if all has been done correctly.


Power
The power behind magical effects is called thaumic energy, measured in units called "thaums." Thaumic energy exists as a naturally occurring ambient field permeating the entirety of the world. It also exists as an internal reservoir of energy available to unicorns. This internal reservoir is created by the physiological processes of life and can be exhausted; it is restored with rest, food, and sleep.


Categorization of Spells
Spells are divided into categories that roughly correspond to increasing levels of power and skill required to cast them. A common joke among unicorn students is that the ranking of a spell refers to how many healing balms will be required to deal with the headache of learning it.
0th Order Spells - extremely simple and elementary spells that most unicorns will know or be easily able to learn. Examples include basic telekinesis and illumination (creation of light). Referred to in casual conversation as cantrips.
1st Order Spells - Straightforward utility spells that almost any unicorn will be able to learn with a bit of study and practice. Many common spells employed in everyday life fall into this category. Examples include magic related to cleaning, cooking, and repairing broken objects.
2nd Order Spells - More difficult spells that are nonetheless available to the average unicorn with concentrated effort and practice.
3rd Order Spells - More complicated and power-intensive spells that the average unicorn will struggle to learn and cast. These spells often affect complicated systems or have applications that could cause harm if done incorrectly. Many examples of healing magic belong here.
4th Order Spells - Extremely complicated and power-intensive spells that the average unicorn will be incapable of learning. Most combat magic is a 4th Order Spell or higher. 
5th Order Spells and above - The most difficult forms of magic, which require intensive and specialized training and high levels of thaumic power.