Trilby

A trilby is a narrow-brimmed type of hat. The trilby was once viewed as the rich man's favored hat; it is sometimes called the "brown trilby" in Britain and was frequently seen at the horse races.

The traditional London hat company Lock and Co. describes the trilby as having a "shorter brim which is angled down at the front and slightly turned up at the back" compared to the fedora's "wider brim which is more level". The trilby also has a slightly shorter crown than a typical fedora design. Provided by Wikipedia