Muggles' Guide to Harry Potter/Magic/Muggle Studies

Overview
Muggle Studies, an optional course, is the Wizarding view of how Muggles live, and the techniques they use to circumvent their lack of magic.

Extended Description
This course is apparently taught by Charity Burbage for the first six years that Harry is in school. The course, specifically designed to teach Wizards how to get along with Muggles, will be required for any Wizarding career which involves liaison with Muggles, including, almost certainly, Ministry jobs.

After Professor Burbage's disappearance, it is taught by a Death Eater, Alecto Carrow, under whose guidance the course seems to have become a diatribe against Muggles, in the best propaganda tradition, teaching how non-Magical people are dirty and behave like animals.

Hermione takes this course in her third year at Hogwarts. As Hermione is Muggle-born, it seems unlikely that she would need to learn about Muggles; but it seems her intent is to learn about how Wizards see and interact with Muggles, rather than to learn about Muggles as such. At the end of this year, despite achieving a mark of over three hundred percent for the course, she decides to drop the course so as to have a humanly possible course load.

Analysis
A certain amount of humour is created in the series by the Wizarding world's residents and their inability to understand Muggle artifacts and techniques. We see this first in Hagrid and his problems dealing with the Muggle train system. It continues with Mr. Weasley's infatuation with electricity, the Weasley family's odd attempts to deal with the telephone and postal system, and the odd assortments of Muggle clothing worn by wizards trying to pass as Muggles at various points in the story. Against this, we have to consider that a significant part of the Wizarding population has either sprung from purely Muggle environs, as Harry and Hermione did, or were raised in households with at least one Muggle parent, like Dean was.

Given the above, we must wonder what the point of the Muggle Studies course is. Clearly, even wizards who take that course are not completely able to fit into Muggle society; a wizard as intelligent as Professor Dumbledore apparently feels that plum is a good colour for a suit when visiting a Muggle orphanage. Additionally, it seems that the Weasley children are able to wear Muggle styles without difficulty, despite being raised in an almost entirely Wizarding milieu; at least, when Harry first sees them, he does not remark anything odd about them except for the fact that one of them has an owl in his luggage.

We don't actually ever see this class, as it is one of the classes Hermione takes separately from the Trio, so what we know about the course is necessarily limited. From the name of the course, and the way wizards educated (presumably) by this or similar course-work behave in Muggle society, we have to guess that Muggle Studies amounts to an anthropological overview of Muggle society and technology, probably out of date to some extent, rather than a course on how to conceal oneself in the Muggle world.

Greater Picture
One must wonder, to some extent, why the author chose to create this course, as we never see it taught and it seems to be somewhat ineffective. It seems clear, however, that it is a useful part of a wizard's education. The school years covered by the story, ages 11 to 17, form a critical part of the young human's understanding of the world outside the family home and the opportunities for gainful employment, so there should be at least an introduction to every field of endeavour in the outside world. Muggles, of course, make up a large majority of the population, and the Wizarding world cannot exist in complete isolation, so at least some of the Wizarding world is involved with Muggles, and clearly this course is intended to lay the groundwork for that class of career.

In the context of our story, however, its role is much smaller. None of the Trio plan a career in Muggle relations, so the course, introduced in Harry Potter and the Prisoner of Azkaban, is initially introduced only so that Hermione can receive top scores for the one year, and then drop it for lack of time without materially changing her educational future. After that, its only mention is Voldemort murdering the professor of the course for daring to publish something that disagreed with his own opinion. The latter mention is, of course, little to do with the course, and primarily intended to show Voldemort's inhumanity. Professor Burbage is sacrificed because a professor of Muggle Studies is most likely to write a sympathetic article about Muggles, and also to highlight the fact that Hogwarts and its occupants are not invulnerable.