While JKR has not gone into much detail about what is studied in Ancient Runes classes, over time, the staff and players of Hogwarts Express have embellished this grey area with their own ideas.
For the purposes of this game, a Rune is defined as a letter or a character in a Germanic or Scandinavian alphabet that is believed to have magical properties. However, there are other mystical alphabets throughout the world, such as Ancient Egyptian hieroglyphs.
For the most part, the study of Runes and other alphabets is confined to translating epic poems and casting in Divinations. There also exists a more practical, more dangerous and less common study of Runes involved in the creation of wards, traps and some enchanted items. The study of Runes in this latter field is a very limited and lost one; modern-day Wizards have only a handful of "formulas" left that are stable. Most experimentation in this field, conducted by the Ministry of Magic, has resulted in disaster. Those players who wish to deviate from this rule, either by the creation of their own unique ward or item, through the creation of a new alphabet (or the embellishment of one), should fill out an application or submit a TP proposal to the staff.
Read on about Runic alphabets, limitations, and usage.
Alphabets
This list is by no means comprehensive, but offers a glimpse of what is commonly offered for study in Hogwarts and is used by the British Ministry of Magic. Those characters who desire a proficiency in other alphabets need to detail in their backgrounds how, when and where they learned these other languages. For the sake of simplicity, all magical limitations placed upon Runic languages also apply to all others.
Of Germanic origin: Elder Futhark, Anglo-Saxon Futhorc, Younger Futhark.
Of Celtic origin: Ogham.
Other alphabets exist that influenced Germanic Runes, yet are not commonly studied in Hogwarts or used by the Ministry of Magic in Britain. They include, but are not limited to, the following: Etruscan, Ancient Latin, Faliscan, Marsiliana, Messapic, Middle Adriatic / South Picene, North Picene, Oscan, Umbrian, Hungarian Runes, Turkish Runes, Tifinagh abjad, South Arabian script and Sabaean.
Some alphabets can be considered mystical in nature, yet are not related at all to Runes. These include: Ancient Egyptian hieroglyphs, Ancient Hebrew, Malachim, Sumerian cuneiform, Proto-Sinaitic glyphs, Ancient Greek, Maya and Choctaw.
Limitations
For the most part, Wizard society is not going to be strongly acquainted with the usage of Runes. Like all knowledge of languages, it takes years of study to gain fluency, and given the number of languages that do have a Runic-based alphabet, those who do study the languages often specialise in one linguistic family. To maintain this knowledge takes practice as well - those who simply do not use it for a few years will lose good portions of their vocabulary and need to play catch-up.
Characters who want to study Runic languages (or any mystical, ancient language) need to clearly outline where, when and how they learned these languages. Knowledge of these languages above NEWT level need to be applied for before they will be approved. Please see 'news cur ancient runes' for an outline of what is studied in Hogwarts up to the NEWT year.
Following the NEWT year, the ways in which Runes may be studied are many and various. Those who wish to take on more practical studies - through the art of wardcrafting - can apprentice themselves to artificers or be taught through the Auror training programme in the Ministry. Scholars of Divinations, linguistics and history often conduct a great deal of independent study or join archaeological societies that focus on such matters. Keep in mind that a character who studies alone is less likely to do as well as one that has been working with mentors.
Characters who wish to attain some level of Rune-mastery will need to justify this in a General application. Runemasters can expect to be able to know three languages fluently (perhaps five if the languages are all related), have a knowledge of the majority of stable ward formulas for those languages, know any Divinations skills that are related to the alphabet, and, if so inclined, could write papers or epic poems in that language. Theoretical knowledge of the more dangerous, forbidden art of naming magic is a possibility, if the character has the proper Ministry connections (such as a position as an Unspeakable) or has a close, personal rapaport with a very powerful Wizard like Voldemort or possibly Dumbledore.
Keep in mind, however, that any applications based around this naming lore are likely to be rejected, and any plots related to them controlled by the staff.
Usage
Ah, Runes. The temptation to make things go splodey with them is a powerful one, yet one must keep in mind that control is needed. If the proper steps are not taken, then at best, one has script that is nothing more than decoration. At worst, one will have an uncontrolled and devastating explosion.
Runes are to be considered a component of a more permanent spell-effect. Often they are written on a trinket or a surface, and the inscription that is chosen defines what the spell effect is to be, who it affects and how long it should endure. These Runes are then activated or "charged" with a spell cast by a Wizard and his wand. The creation of these items or wards is a very difficult process that requires time and practice to master. It is not something that is recommended at all for combat, though the usage of premade, Rune-enhanced items is acceptable. These items are available by application only.
There are only a limited amount of formulas available that have proven to be stable over the centuries since they were lost. The creation of new types of wards is a study that often ends in disaster, though it is rumoured that some members of the Ministry of Magic's Mysteries Department has a sect of Unspeakables dedicated to such a task.
Rumours also exist of a time when Wizards were able to use Runes directly in spells, much like one would cast with their wands, using the principles of sympathetic naming magic. This is a lost art, however, because so much has been lost of the original culture and linguistic subtleties. Currently, the Ministry of Magic strictly forbids any sort of practical experimentation in this field outside of an authorised setting, and none of these exist except, perhaps, in the Department of Mysteries. Anyone who attempts to disregard this can expect to face severe consequences, including death, permanent maiming or insanity, or if the Wizard should survive intact, time in Azkaban.
