Madam Malkin's is a clothing shop next to Flourish & Blotts. It sells robes and other clothing, including the standard Hogwarts-required plain black work robes, and dress robes. Madam Malkin, a squat witch who wears mauve robes, and her assistants will tailor the robes to fit right in her shop. Malkin is an archaic term for a crotchety old woman.
