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Pork pie hat is round hat known from 19th century, called that because of similarity with that time pork pie dish. The most popular were from 1830 through American Civil War, but in the 20th century, it was popularized again thanks to actor Buster Keaton, and, after that, thanks to jazz musicians such as Lester Young and Charles Mingus.
The baseball cap is a soft hat with a peak and traditionally was part of baseball uniform. This cap today even symbolizes American Culture. The first version was known as "Brooklyn style" cap. During the time the peak was longer - to protect eyes from the sun - so it's logical that today everyone wears it: truck drivers, tennis players, and police officers.
Sombrero is a Mexican hat famous for its very wide brim, high and pointed crowns and a slightly upturned edge. Over the last several centuries, sombrero and poncho managed to become the iconic part of the Mexican society. Today this hat is worn not only in Mexico but also all over the world.
On of the symbols of conquering the Wild West is, of course, Stetson Cowboy Hat. Because of its high quality it was a head gear of choice for all that roamed the planes of American West in 19th century. You can find out more about history of Stetson hats here.