Muggles' Guide to Harry Potter/Magic/Care of Magical Creatures

Overview
Care of Magical Creatures is a course at Hogwarts that exposes students to various magical creatures, teaching characteristics and useful attributes. 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. The Trio take this course from third to fifth year.

Extended Description
As a birthday present at the beginning of Harry's third year, Hagrid sends Harry a book, The Monster Book of Monsters, which threatens to attack Harry when he unwraps it. He finds that it is the set book (textbook) for his Care of Magical Creatures course.

At the Arrival Feast that year, Professor Dumbledore announces that Professor Kettleburn will be retiring to "spend more time with his remaining limbs", and that the new teacher for Care of Magical Creatures will be Rubeus Hagrid.

Hagrid starts off by teaching about Hippogriffs, but Draco Malfoy insults the one he is talking to and is savaged. Draco's playing up his wounds results in Hagrid losing much of his confidence, and teaching Flobberworms for the entire Autumn term.

Over the course of the following three years, Hagrid, or Professor Grubbly-Plank in his absence, teach Harry's class about a number of creatures (Knarls, Nifflers, Salamanders, Unicorns, Bowtruckles, and Thestrals, for instance) and some not so common (coursework for the entire fourth year concerns Blast-Ended Skrewts, a creature we have not seen before or since).

None of the Trio choose to take Care of Magical Creatures at NEWT level, despite having apparently sufficiently good OWL marks, so we have no information about what creatures students in sixth and seventh year would be exposed to.

Analysis
Examination of "Newt Scamander"'s book, Fantastic Beasts and Where to Find Them, shows that there are a large number of creatures in the magical world that we do not know of. Many of them have useful characteristics as well. It only takes a moment of reflection to realize that students in a school of magic must receive some education about these creatures, as they form such a vital part of daily magical life. Of course, modern urban schools no longer teach courses in animal husbandry, but such courses are still available and still required in more rural Muggle schools, and we can see that the Wizarding lifestyle is, to a large extent, more centered on small villages and rural settings than on residence in the larger cities. We suspect this is because the eccentricities of Wizarding life are less easily remarked, or more easily overlooked, when population is more sparsely distributed.

It is likely, however, that many wizards will not need to know how to work with magical creatures once they graduate from school. This would suggest that the Care of Magical Creatures course might, in real life, be a less popular course than it appears to be in the books: nearly everyone in Harry's year group ends up in that class, and there seem to be very few students dropping the course, despite the Skrewts in Harry's fourth year terrorizing the students. It is explicitly stated that Harry is using the class as a way to meet with, and discuss matters with, Hagrid, at times when the students are otherwise unable to leave Hogwarts castle. This does not explain Draco's remaining in the Care of Magical Creatures course; particularly after the Hippogriff attack, one would expect Draco's father to order Draco out of the class. We can only guess that the author chose to leave Draco in the class to be an ongoing source of conflict with the Trio, and perhaps rationalized it by having Lucius determine that he could cause more trouble for Hogwarts if Draco remained in this class being taught by a half-Giant.

Professor Silvanus Kettleburn remained only a name until the publication of The Tales of Beedle the Bard. In that book, Professor Dumbledore's notes included significant information about Professor Kettleburn's exploits, which included enlarging an Ashwinder to tremendous size as a prop in a school play, an effort that resulted in significant damage to the Great Hall when the ashwinder exploded unexpectedly. This sort of exploit, no doubt, is the reason for Dumbledore's comment about "his remaining limbs". It seems that a certain disregard for danger is a necessary component for the teacher of Care of Magical Creatures, as the creatures involved are often dangerous. Dumbledore may have selected Hagrid for the post partly because of this potential for danger in the subject matter: Hagrid, being half Giant, has a natural resistance to many forms of attack. However, it is also likely that Hagrid's employment as Keeper of the Keys and Grounds, which apparently involved no small amount of familiarity with the Forbidden Forest and the creatures therein, played a role in his selection for the post.

It is noted in the article on the Forbidden Forest that "In order to have Care of Magical Creatures classes, there must be magical creatures; part of the Forbidden Forest's function is to provide a near-by habitat." By the same token, of course, the presence of the Forest and the creatures within it clearly requires some sort of management, which Hagrid is doing for the first two years of the series. Having Hagrid teach the students about the creatures he takes care of is, of course, a logical step for the author. The reader may suffer a small amount of dismay at the removal of the clearly flamboyant Professor Kettleburn, but the appointment of Hagrid to his post does simplify the process of the Trio meeting with Hagrid later in the series.

Greater Picture
Harry does learn a number of valuable bits of information in this course. Notably, what he learns about Thestrals will help him and five others reach the Ministry in Harry Potter and the Order of the Phoenix, and what he learns about Hippogriffs helps him rescue Sirius in Harry Potter and the Prisoner of Azkaban. However, many of the magical creatures Harry encounters and has to deal with in his travels are covered in a different course; Defence Against the Dark Arts teaches Harry about Boggarts, Dementors, Grindylows, and Pixies, for instance, though he does have to learn about Dragons and Basilisks on his own.