Section 9.3
There are two parts:

1) Theorem: 2-bridge knots is the same thing as denominators of rational tangles.
The proof is complicated, but worth reading.

2) Applications of the theorem. It allows to prove many interesting properties of 2-bridge knots, including a complete classification up to equivalence. 
You can take the theorem as black box and learn about its consequences.

You can indeed do both but it is a bit too much give the timeframe of the lecture. Neither topic is necessary to follow the rest of the course.


Section 9.4
I suggest to skip this section.