Muggles' Guide to Harry Potter/Magic/Hippogriff

Overview
A hippogriff is a creature that has the "body, hind legs, and tail of a horse; but the front legs, wings, and head of what seemed to be a giant eagle, with a cruel, steel-colored beak and large, brilliant orange eyes. The talons on its front legs were half a foot long and deadly looking."

Extended Description
In Harry Potter and the Prisoner of Azkaban, we are introduced to Hippogriffs by Rubeus Hagrid, then teaching Care of Magical Creatures. Like many of Hagrid's favorite creatures, Hippogriffs can be dangerous to handle.

"Things You Gotta Know About Hippogriffs"
(as mentioned by Rubeus Hagrid in Harry Potter and the Prisoner of Azkaban)
 * they're proud
 * they're easily offended
 * never insult one, 'cause it might be the last thing you do
 * always wait for the hippogriff to make the first move
 * it's polite
 * try not to blink if you're facing one, hippogriff don't trust you if you blink too much
 * never pull any of hippogriff's feathers, they won't like it
 * to ride a hippogriff, climb up just behind the wing joint

Approaching A Hippogriff
Because they are polite there is a proper way to approach them. "Walk toward him or her, and you bow, and you wait. If he or she bows back, you're allowed to touch him. If he or she doesn't bow, then get away from him or her sharpish; 'cause those talons hurts."

Analysis
In an interview provided at the time of the theatrical release of the third film, the animators responsible for the sequences involving Hippogriffs mentioned that they had very little to work from. Hippogriffs are mentioned in Muggle mythology, and are described but apparently very rarely depicted. Given this, there is some question as to why Hippogriffs were selected at all. Looking at the story, though, we see that a means was needed to effect an escape for Sirius Black, one that would allow him to travel out of England relatively quickly. With the alarm raised in the magical and Muggle worlds, about his only means of escape would be a magical flying object. Harry's broom, of course, is right out; while Sirius had bought it for Harry, it would have been far too much of a wrench, and far too hard to explain, if Harry were to give that to Sirius for him to escape on. So we must have some other means of flying Sirius away. We have not seen flying carpets, and as it turns out we will not; there is some reason for disallowing their importation, as we find out in Harry Potter and the Goblet of Fire. Sirius has given his flying motorcycle to Hagrid, and Mr. Weasley's flying car is likely no longer up to a long trip, even if it ever does forsake its home in the Forbidden Forest. So we must bring in some other means of flying; and the author, apparently, went through Muggle mythology to find a creature that could fly and was large enough, and possibly even-tempered enough, to be ridden. The characteristics of Hippogriffs, as mentioned above, are pure invention as far as we can tell, but they are very apt, as they reflect aspects of Hagrid's character that we are only now beginning to appreciate, and result in illumination also of the characters of Draco Malfoy and his father. Additionally, they provide the set up for much of this story's secondary theme of the meaning and value of friendship, and allow for Buckbeak's departure without particular repercussions.