Wiki’s definition of Hoop http://en.wikipedia.org/wiki/Aerial_hoop
When I first began investigating lyra, Simply Circus had some of the best resources on the interwebs. I definitely suggest you start with reading these.
General FAQ from Simply Circus http://community.simplycircus.com/tutorials/aerial/aerial_arts_faq.htm
Hand Care from Simply Circus http://community.simplycircus.com/tutorials/aerial/aerial_arts_faq.htm#Hand_Care_for_Aerialists
Instruction Manual — I looked for weeks for a manual on lyra/aerial hoop. There is one – just one – book I’ve been able to find, and it’s in French. But, the majority of the content is in illustration. No high school French needed to make it useful. The site that sells this book also has a lot of great cirque supplies. They are located in the U.K. – so be prepared to shell out some serious cash.