Brandon is correct, the OpenVSP Workshop slides are the only source of theory documentation for VSPAERO. The treatment in that format is pretty top-level, many of the details are omitted.
I have seen many efforts by students to write about VSPAERO. Most of those efforts include a theory section. Since there is no official theory document for VSPAERO, the students end up using information from standard textbooks.
Unfortunately, those writeups end up way off track. Personally, I feel that those writeups are a waste of effort. I understand why you think you need to write up the theory of VSPAERO -- and I understand why your advisor may direct you to do so. However, it isn't something that can be done in a quality manner with the information available.
Someday Dave will write an authoritative theory paper for VSPAERO. After that time, students will be able to plagiarize an accurate description of the theory and methods of the code. Until then, they will continue to make up a fantasy theory document.
Whatever the case, when you find one of these documents out there (that claims to be a writeup of the VSPAERO theory -- that is not written by Dave Kinney) -- know that it is wrong and you shouldn't believe anything it says.
Rob