This information is primarily for my ATS bellydance students, but other dancers might find these resources useful as well.
Music Theory by Mary Ellen Donald. This is a brief, clearly written article that defines basic music terms like "rhythm" "measure" and "time signature." This extremely helpful for communicating about music with other dancers or musicians.
Carolena's Music FAQ for ATS is less about music theory in the technical sense, and more about the theory behind our choices for music for ATS. In this article, Carolena lays out what music is most appropriate for ATS, and also explains other points, such as how it is that we use slow moves with songs that have a fast tempo. Throughout the FCBD CD catalog, tracks are labeled with fast, slow, and sometimes a description of the piece. Very helpful!
Zill Speak by Artemis Mourat is a fantastic CD that comes with a booklet. She breaks down rhythms very clearly, with a variety of techniques to remember them by. While not all the rhythms are relevant to ATS, they are all common to Middle Eastern music, and therefore good to know!
Learning about music theory is definitely an ongoing process. It takes some initiative to investigate the variety rhythms and instrumentation to flesh out your knowledge. While there are tons of resources available for learning the basics, there is no replacement for just sitting down and listening to A LOT of music!
Here is a jumpstart to music for ATS! I've made an iMix featuring my favorite songs for drilling and dancing: