For 'low level', I mean those are more familiar and intuitive to me, such as integers should be much more 'low level' than the general definition of rings, or groups.
It is so often that I do not know why some concepts are important when I am studying some 'high level' mathematics (e.g. In topology: separable? second countable? Why are mathematicians studying them? Will they show up repeatedly in the world of mathematics? What are some interesting facts about them?).
Most books surely give examples, but many of them are not familiar, not 'low level' enough to me.
Let say what kind of book is considered to be 'good' for me. I think it is good if a algebra book start with some elementary number theory and then introduce the concept of group/ring (as my lecturer did), because elementary number theory is so familiar and intuitive to me (to everyone also, I think), that will make me surprised, extremely motivated and wonder:'wow, I didn't know we can consider these familiar results in such a new and powerful point of view!'. But unfortunately, those kind of book is not easy to find.
Could you please name some resources(books, papers, etc.) that introduce 'high level' concepts with 'low level' examples/facts?
Have you seen this before: https://en.m.wikipedia.org/wiki/Furstenberg%27s_proof_of_the_infinitude_of_primes
It is a proof that there are infinite primes ("low level" result) using "topology".
The reason I put quotes around "topology" is that upon deeper inspection the proof is written in topological language but there is nothing much topological about it.
Hope you find it interesting though. I certainly was amazed by it.