|Spoiler Alert: This page contains spoilers. Read at your own risk.|
Engravement Magic is a magic technology somewhat similar to Casting Assistant Device (CAD) technology. The engraving techniques create geometric patterns on various items thus enabling the user of the item to cast a spell by channeling Psions into the pattern. Magic Geometry is theoretical base for forming these patterns, which is part of the magic high school curriculum.
"No luck. Apart from the handle it's totally hollow. It increases strength by using the technique of carving seals into it.
Reinforcement magic is your field isn't it?"
"...The technique takes a geometric pattern and engraves it into a sensitive alloy, which activates by injecting Psions, right? If you do that, wouldn't it bleed a considerable amount of Psions? You'd run out of gas pretty often wouldn't you? Carved seals are pretty inefficient in the first place, so I thought it's not a technique used very often nowadays." 
Engravement magic applies geometric patterns to a sensitive material which after being injected with Psions casts a magic.
It is said during the fights that broke out after the terrorist attack on First High School:
"That guy, even his magic is old school..."
Erika snarled furtively, pretending to be ignorant of the fact that her Engravement Magic was also a type of magic prevalent in the past.
Thankfully, Leo didn't catch these words while he was locked in combat. 
Engravement magic is considered a somewhat obsolete technology. However, it has the benefit of being usable under Cast Jamming, too:
Even so, Erika's CAD was a specialized model that was fortified for high speed combat and possessed a form that Erika was well accustomed to. In addition, her Engravement Magic was a type that could still channel Psions even under the effects of Cast Jamming. 
Before the newcomers' Monolith Code final Shiba Tatsuya informed the students present about the auxiliary equipment he was about to use in the match:
"I don't believe there will be a problem since we handed in the CADs in time. The rule book didn't say that we are forbidden from wearing uniforms inscribed with magic themselves."
Hearing his answer to Miyuki, the number of "?" marks on Mayumi's head increased by one as she asked Tatsuya.
"Correct. This is done by combining the principle of Engraving Magic with the mediums from Ancient Magic. The mantle and robe include enchantments that facilitate the user using magic." 
It is mentioned that the Isori Family is actively practices Engravement magic and develops magic tools that make use of it:
After leaving the examination of the mantles and robes to Isori (the Isori Family were renowned for their expertise in Engraving Magic, not that Isori himself hid his personal interest either), Tatsuya left the pavilion to relax himself. 
"My CAD was also developed by the Isori Family. Speaking of which, didn't Isori-senpai make it for me?"
Speaking of which, Erika pulled out her CAD that was shaped like a retractable police baton out of nowhere.
"Well, I guess... But only the 'Engraving' portion."
"You designed the Engraving spell yourself? That's incredible..."
"Kei is a genius!" 
The Isori Family often co-operates with the Chiba Family in development of magic equipment (see previous quote and the following):
As she ran, Erika reached into the thin, long box she wore over her back and pulled out a naked sword that was not sheathed. As a replacement for the blade, the entire body of the blade was covered in engravings, given that it was a weapon forged by the Isori Family. This was a gift from Isori Kei to Erika as a replacement for the overly conspicuous Orochimaru. While unable to achieve the same power as Orochimaru, it was still equipped with the ability to execute Inertia Cancel. 
Engravement magic has its roots in Ancient Magic as it can be understood from:
The "formation" that Isori spread underground was also able to detect the enemy on the surface. The surface and insides were covered with diagrams, created with silk threads, that aided in magic invocation, which was essentially a magic formation.
As an elite of the Isori Family, who were the authorities on Engraving Magic, Isori Kei excelled in this sort of magic which was unimaginably similar to the ritual formations used in Mikihiko's Ancient Magic. In the end, no matter whether it was modern magic or Ancient Magic, they differed little on the point of "magic".
Hence both of them were fulfilling similar roles, which on some level made perfect sense. 
The object that appeared to be an iron fan contained thin, paper-like strips of metal linked together at a single point. Each strip of metal was covered in engravings of various incantations and formations. These strips combined to form the iron fan that was the conduit for Psions favored by practitioners. The tassel extending from the fan went all the way into the sleeve, where it was connected to the device containing the Activation Sequence that replaced any need for incantation. 
For wood or stone based golems, they are often used in the engraving magic technique to affix the magic type. 
Engravement magic was also the research theme of First High School's Thesis Competition presentation in AD 2096:
“——This way, there isn’t any need to position a sensitive alloy plate at the ‘engraved’ part in order to activate the engraved type magic. ‘Engrave’ is intended only to induce Psion flow, as we can see right now at the projected image, the same pattern of ‘engrave’ can be obtained after the Psion’s fill in. The essence of engraving magic, as you can see, does not depend on the engraving itself.”