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Arithmancy is a branch of magic that is concerned with the magical properties of numbers; someone who practices Arithmancy is called an Arithmancer. For example, in the 1200s, Bridget Wenlock, a famous Arithmancer, discovered the magical properties of the number seven (fw22). An O.W.L. in Arithmancy is required to apply for a curse-breaker's job at Gringotts' (OP29).
Arithmancy at Hogwarts is taught by Professor Vector. In her class, students are expected to write essays and to be able to understand complicated number charts, which are part of their homework (PA12). Hermione Granger appears to be the only Gryffindor in her year who attempted an O.W.L. in this subject (which is her favourite) (PA12, PA16).