Cool Jazz is a type of jazz that is understated and subtle. It has nothing to do with beatnik or folk music. West Coast Jazz (often considered an invalid jazz type as it encompasses more than the west coast of the USA) is often part of Cool Jazz. The Claude Thornhill Orchestra and Lennie Tristano first recorded Cool Jazz in the late 1940s. Thornhill's most popular song Snowfall is still played today.
Other examples of Cool Jazz: