Controller postion on page 3 of lecture notes.

I think the controller C(s) is not in the right position. Shouldn't it be in the feedback part of the loop?

No, the lecture notes are correct as they are printed. The controller takes in the error (difference between output and reference) as an input and outputs u (the control signal). The formula for the closed loop transfer function is correctly stated using the form printed in the lecture notes as PC/(1 + PC).