I've been playing mandolin now for around 8 years. I learned mandolin by way of fiddle tunes which can really help the beginning player learn how to put runs and scales together for all kinds of songs. I love to play bluegrass and I also love to play many kinds of jazz - one particular favorite of mine is swing-jazz ala Django Reinhardt.
People don't usually associate mandolins with jazz, but used skillfully, they can really compliment a small jazz ensemble.