"pure" explanation of Reed-Solomon? I encountered two applications of RS codes - one in group testing, and another time someone said that a solution to an interview question was using it. But when I search for explanations, it's all about the cracks in the CD disks and such. Is there a good source that puts the math first?
Jon Hall's coding theory notes, available online here are quite good. See Chapter 5.
In addition, see Blahut's text Algebraic Codes for Data Transmission where more focus on decoding algorithms is present.