The mandolin is an accepted and much loved part of folk and country music, adding the characteristic double-course treble to a tune either as single note picking or the sometimes cliched tremolo that reminds one of the origins of the instrument in Naples. (Think of 'O Sole Mio').
Mandolins come in a variety of styles which generally reflect their use in different types of music. In truth, they are interchangeable but their construction and sound quality make them better suited to certain music.
Bluegrass and Country favour the f-style while folk musicians favour the a-style. The old original bowl-back is favoured by classical players.