One of the most important musical styles of Azerbaijan is that of the mugham. It’s basically a long segment of sung poetry with musical interludes between the segments. They will also utilize a form of yodeling as well. The poems these are based off of are most about a divine love that is often sourced from Sufism and originated in Iran.
Some of the common instruments you’ll find in Azerbaijani music are the tar (a type of lute with a double bowl), kamancha (a bowed string instrument similar to the rebab), the oud (a short-necked lute), and the saz (a long-necked lute). There are also a number of drums that are used: naghara (cylindrical double-faced drum), goshe nagara (pair of small kettle drums), ghaval (frame drum), daf (another type of frame drum), and the nagara (a barrel drum).
I found this video of the ashik style music. I believe what the performer is using is a saz (please correct me if I’m wrong here). You can definitely hear the “yodeling” style when he sings, although there are times when it's almost sung-spoke. Although I have no idea what he’s singing about, at times I get the feeling he’s the Bob Dylan of Azerbaijan.
It was somewhat harder to find current popular musicians. This year the Eurovision Song Contest was held in Baku, and I did find a singer named Emin Agalarov. (Spotify, I'm wagging my finger at you for not having any of his stuff.) This video is of the finals from the 2012 Eurovision and showcases some of the mugham concepts mentioned above as well as showcasing current pop music. You’ll be able to pick out some of the instruments mentioned as well as the drums.
Azerbaijan has a number of folk dances that have developed over the past centuries as part of its national culture. Asma Kasma is one of the oldest dances, one that’s used when the people escort a bride to the groom’s home. It’s generally somewhat slow and includes a lot of exaggerated jumps.
The Halay (also called Yalli in Azerbaijan) is a dance that’s centered around fire. Fire is and has been an important symbol in Azerbaijani history. It starts out slow, but speeds up to where the steps are almost running.
The Uzundara is a slow, attractive dance danced solely by women. It’s origins lie in the Karabakh region and traditionally is danced and sung while the bride and groom are away. It reminds me a little of ballet at times.
The Zorkhana is a men-only dance that is used to signify courage and valor. However, this video made me smile. Perhaps the courage and valor comes in the form of actually getting the guts to go out there and dance. To all the nerdy guys at frat parties in college we laughed at because we thought they couldn't dance, well, apparently they one-upped us: they were beyond us all the whole time dancing the zorkhana.
Up next: the food!
Wikipedia: “Music of Azerbaijan” “Dances of Azerbaijan” “Mugham”