I believe the confusion from the OP was that if you don't already have significant mathematical maturity (in the sense of having seen bits and pieces of number theory, linear algebra, and group theory before) you'll quickly be frustrated trying to follow along as you won't be able to reason at the necessary level of abstraction.
>Is "number theory" an appropriate title
I think "number theory from first principles" is a misleading title, and I almost skipped over it because I thought it was yet another introduction to modular arithmetic, congruences, and such. Instead, the bulk of the article lays summarizes the main results in number theory/group theory that can be put into practice to construct cryptographic primitives so I think titling it "Foundations of Cryptography" might be better.
- Is "number theory" an appropriate title? Should it be called "linear one-way functions explained from first principles"? Or "abstract algebra"? Or "math behind modern cryptography"? Maybe. But I think I made it quite clear in the introduction what the article is about. If you were looking for something else, feel free to leave again.
- Should I have introduced modular arithmetic and the groups of integers modulo some number before finite groups in the abstract? Maybe, but I also explain my reasoning behind this order in the introduction. As mentioned there, you get to these examples by scrolling just a bit.