Forerunner symbols

In the Halo Universe, there are many Forerunner Symbols -- that is, pictograms made by the Forerunners. These symbols can be found above doors, on Elite armor, virtually anywhere on the Installations, and in the Covenant.

Usage
The exact nature of Forerunner writing remains a mystery. The symbols are most likely logograms, rather than parts of an alphabet or syllabary. There also seems to be more dimensions to Forerunner writing than traditional methods, with the individual glyphs holding multiple meanings, likely making them entirely contextual -- when combined with different glyphs, a symbol might have radically different meanings, making individual glyphs pictograms or ideograms.

Other symbols found on Forerunner relics and structures are even less obvious in their meanings. They are obviously decorative in nature, but they are often larger and more elaborate in nature than their glyphs, and may depict specific shapes and forms, and may have more in common with petroglyphs than logograms.

Symbol Analysis
The symbols are primarily composed of circles and curves. Each glyph appears to use a circle as a base shape, often combined with either a concentric circle or fragments of one. Another common trait is the presence of one or more circular arcs whose osculating circles' centers lie on the base circle. Non-circular arcs and small non-concentric circles can be seen on some glyphs. The filling in of areas is uncommon but has been seen in Forerunner glyphs.

According to Bungie employee Joseph Staten, the blue and red signs denote the safety of the area -- that is, whether or not the Flood are there. Taking a closer look at the symbols, their locations, and what has been said by Bungie, we can deduce the following:

All of the others are found in various Forerunner structures, mostly on the levels 343 Guilty Spark, Silent Cartographer, and The Library.

Cropped Symbols Analysis
Several of the symbols are variations of each other. There are a total of 16 unique symbols; the other 8 are rotations or croppings of the 16 main symbols. Of note is the fact that the cropped versions may not have been intended to be cropped; their in-game textures may have been inadvertently placed such that they extended beyond the edges of the polygons they were on, causing the parts that couldn't fit to be clipped. For sake of being thorough, however, they have been included as separate symbols.

One could speculate that the orientation of the symbols changes their meaning in some way, like verbs in English (run - running - ran - runner - etc.).

Numbers
Only the Forerunner symbols for numbers one through five are known, though a base symbol with unknown meaning has also been found. It is probable that they also have a symbol for 0, but they may use a base 6 system and not have any more numbers. The base symbol may be the number 0, or the Forerunners may not have had a number zero.

The visual features of numerical glyphs differ slightly from those of normal Forerunner glyphs. Like the other glyphs, numerical glyphs use a circle as a base. However, the only features seen on numerical glyphs are concentric circles and arcs, radial lines, and the occasional radial line with a small circle on its end.

Installation Symbols
In Halo 3, a number of details about the Halo Array arise. In the Ark's Citadel, where the Prophet of Truth is preparing to fire the seven Installations, each Installation is shown in detail. Each Halo has its own hologram showing its structure and status, as well as a holographic symbol identifying each Installation. Some notes say that there are two versions of each symbol, one where you enter the ring room and the view from the pedestal.

Shield Worlds
Several symbols have appeared throughout Halo 3 and on the cover of Ghosts of Onyx. In the book, it was described as the symbol of Shield World, but the symbol is also seen on top of 343 Guilty Spark and behind his "eye". It is also seen in the Terminals.

Trivia

 * It is unknown if the Mark of Shame is a Forerunner Symbol.
 * The base numerical glyph was used as an avatar by AdjutantReflex.
 * There is at least one Forerunner Symbol that matches the Marathon Symbol.