Sigil

A Sigil (シジル) is a magic symbol used to represent certain subjects according to Idol Theory. Most often in Western magic, it represents an angel.

Etymology
Sigil is derived from the Latin sigillum, meaning "seal."

Principles
Sigils represent things from a special cross, to that of Hebrew alphabets. The lines used in a sigil are used to display a word. However, it is most often used to display a name of an angel in order to obtain Telesma. What the sigil draws out depends on the angel the sigil represents, like Archangel Gabriel representing the direction of south, which the spellcaster may use to tell others which direction to go.

What they represent seem to imply that they can also be used in magic circles, for when writing the name of the angel whom the spellcaster desires to borrow the from, among other functions, instead of regular alphabets.

As Silvia demonstrates, there is no reason for a sigil to be solely written on paper or on the ground - they can also be formed through various movements, like using a rope to signify the sigil of Archangel Gabriel.

A common tool used by both members of the Rosicrucian Order and the Golden Dawn is a rose cross medal, which acts as an all-purpose spiritual item that can mass-produce sigils, extracting the name of an angel or spirit by spelling it out in one stroke. Each of the rose's petals has one of the 22 Hebrew letters engraved on them.

Toaru Majutsu no Index: Mars SS
After being taken hostage by Bisai Otome, Index left behind sigils to tell Kamijou Touma and Fleiss which direction to go in order to follow her.

Toaru Majutsu no Index: Kanzaki SS
During the confrontation between Kanzaki Kaori and Leivinia Birdway as the two were going after Orlentz Trice and losing their tempers, Birdway ordered Mark Space to bring her a magic sword, intending to take Hebrew text from a cross medal and draw a sigil to use against Kanzaki.

Toaru Majutsu to Kagaku no Ensemble
During Tsuchimikado Motoharu and Kanzaki Kaori's investigation of the other magician intruding into Academy City, the former discovered that sigils were present in Rondo Net's user agreement.

Ichihanaran Festival Arc
Silvia made use of sigils during her battle with Thor.

Coronzon Arc
During the events surrounding the Crowley's Hazard invasion of the United Kingdom, it was mentioned that sigilized names might be carved on surface of Ange Catacombs' autonomous suitcases. When accessing the internal 'contents' of the Anti-Art Attachment's components, Coronzon recognized that there were ordinary sigils incorporated into them.

Trivia

 * Besides the Hermetic Rose, another tool used in creating a sigil is a (some known as kameas) - a grid with specific numbers. In much the same way as with the petals of the rose corresponding to Hebrew characters being used to trace a sigil, the characters of the subject are converted to number form and the positions of those numbers on the square are used to draw the sigil.
 * In some cases where sigils, such as those derived from the rose, are depicted and drawn, a small circle is used to mark the starting point of the sigil's line and a small perpendicular line is used to mark the end point.