Professor: Defense Against the Dark Arts
Ministry: Auror (former)
Clearly, there are two Mad-Eye Moodys. There's the Mad-Eye Moody who is the noted Auror (a.k.a. a member of the Ministry who captures Dark wizards), and there's the Death Eater Moody (a.k.a. Barty Crouch, Jr.) we meet in Goblet of Fire. (Be sure to check out our analysis of Barty Crouch, Jr. for all the details on him.)
Moody bears tons of scars from his career fighting the Dark Arts, including a chunk taken out of his nose and a peg leg. He's got the famous mad eye too: a perfectly spherical blue glass eye that helps him see everywhere, even out of the back of his head and through Invisibility Cloaks.
We only meet the true Moody at the very end of the novel, so we're not really sure what he's like as a person. However, we have to assume that Barty Crouch, Jr.'s characterization of the real Mad-Eye Moody is pretty accurate, since no one notices anything off about "Moody" at all. But, in truth, the real Mad-Eye Moody has been kept in a trunk for the whole school year, and it's been the Death Eater Barty Crouch, Jr. who has been befriending Harry Potter and turning Draco into a ferret. So, given that we're assuming things about Moody based off of Barty Crouch's amazing performance, here's what Moody is like:
Moody is famously suspicious and keeps up a regular cry of "CONSTANT VIGILANCE!" (14.35). And he has no patience at all with anyone who has ever been associated with the Dark Arts, including Professors Snape and Karkaroff and, of course, Draco Malfoy. (The ferret incident is pretty sweet.) As he tells Harry, "Oh if there's one thing I hate [...] it's a Death Eater who walked free" (25.163). Moody is serious about instructing his students about the realities of the Dark Arts, and he does it grimly and effectively (unlike pretty much every other previous Defense Against the Dark Arts instructor, with the exception of Professor Lupin).
Mad-Eye Moody is gruff and forbidding. But he's also kind at heart. When Neville Longbottom looks miserable after seeing a demonstration of the Cruciatus Curse (which drove both his parents insane), Moody brings him to his office for a cup of tea and a chat about magical plants, which Neville loves.
Still, at the end of Book 4 we are left wondering if our impressions of Moody are at all accurate. Guess we'll have to read Book 5 to find out….