Battle Magic was the other group of spells, the ones for fighting, and encompassed both the sort of things you might learn in a Hogwarts Defense Against the Dark Arts class and also the sort of things you were supposed to be defending yourself from. In Battle Magic class, there was always a professional Healer on hand in addition to the stern professor, which confused Hermione until the first time she saw a classmate mispronounce a hex and accidentally rip his partner's wand arm clear off. (Hermione had had to shut her eyes and take deep breaths for several moments before being able to resume practicing herself.) She did not like Battle Magic at all, but did her best at it anyway, because if nothing else she desperately wanted to prove that she was just as good as all these pureblood supremacists she was surrounded by.