The most difficult part of this material for me was following Lemma 8.6. I got a little confused with the difference between a p-group and a cyclic group. Maybe it was just because it is a long theorem but there were some conclusions drawn that just didn't quite make sense to me.
The most interesting part of this material was the Fundamental Theorem of Finite Abelian Groups. When I think about all of the things that come from knowing a group is cyclic and has some characteristic associated with primes, it's very cool to think that every finite abelian group is the direct sum of cyclic groups and each of prime power order.
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