By structural hierarchy, I mean the mental concept in which things are 'done' in mathematics. At the top, you have mathematics itself, which is a collection of systems, like arithmetic, algebra, geometry, etc. At the bottom, you have you axioms, truths which cannot be logically questioned due to their self evident nature.
The problem is that I do not know what goes in between, and in which order. Roughly speaking, I imagine that a system incorporates a group of axioms, used to build proofs, which form mathematical tools, which are used to build the system.
The reason for asking, is that I feel that it would make my study of maths easier; If I can't achieve something in mathematics, whatever it may be, I can try to identify the problem on different levels, maybe my method is wrong, or maybe it's the wrong structure or technique, or maybe am not using the correct system be begin with, and so on.