Question on the hierarchy of named Ordinals

Question

I was wondering how many named transfinite ordinals there are, and what the notations and names are, arranged as a hierarchy which ignores the different levels on a single level of Ordinals (ω+1, 2ω, ω^ω, etc), but rather the ones separately named, I know that it goes up rather high and has many separately named Ordinals, I just want to learn of more of them. And have my misunderstandings corrected.

ω
ε (Defined by where ω^α = α or ω^{ωωωωωω...} or ω↑↑ℵ₀, if that is a valid notation)
ζ
φ
Γ₀ (Feferman–Schütte ordinal)
ω₁ck
ω₁