Aetiology: The study of the causes. For example, of a disorder.
The word "aetiology" is mainly used in medicine, where it is the science that deals with the causes or origin of disease, the factors which produce or predispose toward a certain disease or disorder.
Today in medicine one hears (or reads) that "the aetiology is unknown." Translation -- we don't know the cause.
Aetiology is the preferred spelling in some countries, including the UK, whereas "etiology" without an "a" has taken over in the US. The word "aetiology" comes from the Greek "aitia", cause + "logos", discourse.