The Tyrolean hat is a type of fedora hat

Hat

A hat is a head covering. It can be worn for protection against the elements, for ceremonial or religious reasons, for safety, or as a fashion accessory. In the past, hats were an indicator of social status...

 named for the Tyrol

County of Tyrol

The County of Tyrol, Princely County from 1504, was a State of the Holy Roman Empire, from 1814 a province of the Austrian Empire and from 1867 a Cisleithanian crown land of Austria-Hungary...

 in the Alps

Alps

The Alps is one of the great mountain range systems of Europe, stretching from Austria and Slovenia in the east through Italy, Switzerland, Liechtenstein and Germany to France in the west....

. It is essentially the shape known as the Trilby

Trilby

A trilby hat is a type of fedora. The trilby is viewed as the rich man's favored hat; it is commonly called the "brown trilby" in England and is much seen at the horse races. It is described as a "crumpled" fedora...

. Tyrolean hats are made of felt

Felt

Felt is a non-woven cloth that is produced by matting, condensing and pressing woollen fibres. While some types of felt are very soft, some are tough enough to form construction materials. Felt can be of any colour, and made into any shape or size....

, traditionally having a corded hatband and a feather on the side as trim.

The traditional "brush" worn on the hat is made of the tail of the chamois goat. The brush takes a variety of forms, and may often be combined with feathers.

In literature

It was disapproved of by Jeeves

Jeeves

Reginald Jeeves is a fictional character in the short stories and novels of P. G. Wodehouse, being the valet of Bertie Wooster . Created in 1915, Jeeves would continue to appear in Wodehouse's works until his final, completed, novel Aunts Aren't Gentlemen in 1974, making him Wodehouse's most famous...

 and eventually relinquished by Bertie Wooster

Bertie Wooster

Bertram Wilberforce "Bertie" Wooster is a recurring fictional character in the Jeeves novels of British author P. G. Wodehouse. An English gentleman, one of the "idle rich" and a member of the Drones Club, he appears alongside his valet, Jeeves, whose genius manages to extricate Bertie or one of...

 in Stiff Upper Lip Jeeves in the PG Wodehouse canon.