Magic

Magic (魔法 mahou) is a miracle other than Magecraft, the final achievement of a magus, the ability to make possible something that is impossible to realize in the current era. If a given person, or group thereof, is able to realize "magic" regardless of the time and fund put into it, then the "result" isn't magic. The ability to realize that impossible achievement is this miracle named magic.

Back when civilization was young, most of the magi were magicians, but only five are left now. Or rather, only four magicians are still alive: the magician who used what is called the First Magic has died already. Of the remaining four, two are still unclear, but two are frequently spotted as they travel around - although they are more of a nuisance to the others.

Source: Fate/Side Material encyclopedia entry (p.75)

The major sites (Mirror Moon, Moonlit World, Fuyuki wiki) usually translate mahou as either Magic or True Magic, and refer to their users as Magicians.

There are currently 5 known Magics.

The First Magic

 * Name: Unknown.
 * Territory: Denial of nothingness.
 * User: Died a long time ago, but it is still said that there are 5 Magics. According to Tohsaka Rin, Emiya Shirou may have used it once in the Heaven's Feel route of Fate\Stay Night

The Second Magic

 * Name: Unknown, referred to as either "Zelretch" or "Kaleidoscope".
 * Territory: Operation of parallel worlds.
 * User: Kishua Zelretch Schweinorg. Tohsaka Rin uses fragments of it in the Heaven's Feel route of Fate/stay night.

The Third Magic

 * Name: Heaven's Feel, Cup of Heaven (天の杯).
 * Territory: Materialization of the soul.
 * User: If it can be considered to have any user, it would be Lizleihi Justizia von Einzbern, who is the core of the Great Grail, and Illyasviel von Einzbern although she cannot use it properly.

The Fourth Magic

 * Name: Unknown.
 * Territory: Unknown.
 * User: Unknown.

The Fifth Magic

 * Name: Blue
 * Territory: Unknown. It is also not known if Aoko's specialization in destroying things is related to her use of the Fifth Magic.
 * User: Aozaki Aoko.