I recently tried (again) to understand hierarchical structures as they occur in mathematics. I started with directed graphs and thought about the notion of a minor.
Next I read about groups, the group extension problem and homological algebra (interesting, but a bit too advanced). Then I worked through some material on semigroups (arduous...), and learned that lattice theory might be interesting for me. So I worked through some material on universal algebra, which also covered the basics of lattice theory (very interesting and rewarding). I think I found more or less what I was looking for, so I won't search any further. Instead, I will consolidate what I've learned so far and fill in some minor gaps.