A general term for those who use magecraft, regardless of nationality or field of study.
They don’t get along well with the Church, and the two groups are constantly feuding behind the scenes.
However, they have pretty much nothing to do with the plot of Tsukihime. If you want more details, please refer to Kara no Kyoukai.

Tsukihime Data Collection: Tsukihime Dictionary

Wizards. In Fate/EXTRA “Wizard” refers to A-class hackers.
Compared to your average hacker, wizards posses special abilities and can dive into the cyber world at a soul level.
Ordinary hackers fall into two categories:

- Visual Perception Digitization (only visual)
(This is done through a simple spinal insert interface connection.
Information is directly streamed into the brain, so they avoid the trouble of transforming each type of information into a digital signal. Favors input only.)

- Visual and Touch Perception Digitization.
(This is done through a wired connection from the nerves to the net. It allows a hacker to project the basic components of their being onto the net. Input/Output capable, and more powerful.
However, the user is unable to project a human form in the cyber world.
This is at best a simple projection, and as such is not recognized as a life form. Their existing circuit is read from their body, and they just manipulate that projection. They are unable to change or revise their circuit.)

However, wizards are capable of far more than that, they can digitize and spiritize their consciousness and physical body, creating a copy that is sent inside [the cyber world].
It is the materialization of soul inside the cyber world.
As for cyber bodies in SE.RA.PH, they refer to the spirit form of three components: body, mind, and soul.

Hacking knowledge and skills are not particularly important for wizards, physical ability and mental prowess are far more useful.
Having magic circuits (also known as imaginary nerves) in your body, and the ability to clearly conceptualize your digital self is essential to help translate the true essence of yourself accurately into a digital image in the cyber world.
The way of conceptualizing one’s digital image differs from wizard to wizard.
There are a variety of methods; some use computer processing,
others use meditation to give birth to their image,
and some even take drugs to escape from reality.
In present day 2030 Viritual Spiritron hacking has become possible through an external interface, but magus-class hackers remain a rarity.
Due to magus having human rights, even the West European Plutocracy couldn’t monopolize them. Aside from those under the control and management of the United Nations, there remains a never ending list of countries who try to harbor free magus behind closed doors.

The definition of life is considered to be “the ability to change the environment you live in through your own actions and of your own accord.”
Since wizards can intervene in the cyber world through their souls, Moon Cell accepts them as living, and thus their advance into the cyber world is possible.
Pioneering, expanding to new frontiers is, in a way, the greatest meaning and sin of mankind.
To wizards who posses this ability, it’s not too much to say that the cyber world is like a second reality.
A physical body is merely a “home” of sorts to a wizard.
If the physical body of a wizard on Earth were to die, it would simply mean that they would not be able to return “home,” and they would remain in the cyber frontier. As long as their existence in the cyber world is not destroyed, their soul would not disappear.
(However, the empty shell that is a Wizard’s real physical body protects them from change in the cyber world, and the loss of it will quite easily and unavoidably transform the structure of their intelligence, as well as their sense of values.)
To a wizard, the only true death is the death of their cyber existence.
Only after their souls have burned out and crumbled away will they become scrap that is no longer able to be revived.

Translator's Notes
  1. ^ In Fate/EXTRA Material, this entry appears under the あ section (instead of ま).
Fate/EXTRA Material: Encyclopedia of Fate/EXTRA

One capable of wielding magecraft. Mages pursue mysteries, and strive to reach the Root.

MB Back Alley Alliance Nightmare: Encyclopedia of Rojiura Nightmare