Muggles' Guide to Harry Potter/Magic/Ancient Runes

Overview
Ancient Runes is the study of runic writing. Runes are characters designed to be scratched onto hard surfaces such as rock, and are almost entirely made up of straight lines. This subject is offered as an elective, taught in years three, four, and five; those with sufficiently high O.W.L. marks in the course can then go on to N.E.W.T.-level study in years 6 and 7.

Extended Description
We first hear mention of Ancient Runes as a course in Harry Potter and the Chamber of Secrets, around Easter. The first two years of Harry's education have been taken up with the basics: Defence Against the Dark Arts, Potions, Charms, Transfiguration, Herbology, History of Magic, and Astronomy, with Flying taking the place of Muggle physical education. As the beginning of the third year approaches, students must choose a set of electives to add to these core subjects. Hermione chooses all the available subjects, including Ancient Runes, and stays with Ancient Runes until the end of her time at Hogwarts.

Hermione makes use of her understanding of Ancient Runes in Harry Potter and the Deathly Hallows, where she is bequeathed an ancient copy of The Tales of Beedle the Bard. It is her ability to decipher these runes that allows us to hear the Tale of the Three Brothers, and so become enlightened in the nature of the Deathly Hallows.

As only Hermione takes this class, we do not see any of it. It is possible that it is taught by Bathsheba Babbling, but we never meet the professor of the course.

Analysis
The sole purpose of the introduction of this course seems to be to allow Hermione to be able to read the copy of the Tales of Beedle the Bard bequeathed to her by Professor Dumbledore. One would think that the purpose of this legacy could have been equally carried out by a version of the book written in English. However, creating of the book in runes serves two purposes. First, it indicates in no uncertain terms that the book is extremely old, being written in an alphabet no longer used. This serves, among other things, to reinforce that the tales in this edition are as close to the original as is possible. Second, it requires Hermione to spend time trying to figure out the meaning of the sigil of the Deathly Hallows as it appears over the one tale in that book, requiring that she bring Harry into her thoughts about the symbol, and thus connecting it to Grindelwald's mark, Xeno Lovegood, and the signature on one of Dumbledore's letters as reproduced in Rita Skeeter's book.

The only other place we see ancient runes is on Dumbledore's Pensieve. Though Harry notes them, we don't think Hermione ever does, and they play no part in the story except as decoration, and possibly an indication of the Pensieve's age.