As I said in class, the book is more written for mathematicians who want big more general theorems, and the book throws in more superstructure in places than is needed for the cryptography. In class I have often chosen simpler routes to important results for cryptography. Here specifically are book topics that you are not responsible for:

Ch 1. Have the result, but no need to reproduce the proof that O(xgcd(a, b)) = O((bits in a)(bits in b))

Ch2 definition of monoids and semigroups, and for now, skip 2.14, 2.16,2.18-end.

... More in later chapters added later.