User blog comment:Deedlit11/Ordinal notations II: Up to the Bachmann-Howard ordinal/@comment-11185268-20130628211056/@comment-5529393-20130629001039

I'm glad you're interested! For an introduction to ordinals, you can check out Baez's article

http://math.ucr.edu/home/baez/week236.html

and his bigness articles on Google Plus, for example

https://plus.google.com/117663015413546257905/posts/J52v1WXoRA1

Also, check out David Metzler's excellent video series on large numbers and ordinals starting with

http://www.youtube.com/watch?v=QXliQvd1vW0

Parts 1-3 are on Knuth and Conway notation, he starts talking about the fast-growing hierarchy in part 5 and ordinals in part 6.

However, he doesn't get to ordinal collapsing functions; for a discussion of those, you can read

http://en.wikipedia.org/wiki/Ordinal_collapsing_function

However, I don't know if this is easier than what I wrote. You can also read

http://quibb.blogspot.com/2012/03/infinity-impredicative-ordinals.html

but there are some mistakes,