Below you can find notes for the class on PCPs and hardness of approximation I gave at MIT in Fall 2010:
https://stellar.mit.edu/S/course/6/fa10/6.895/index.html
Introduction
1. Approximation, hardness of approximation, the PCP Theorem (two lectures)
PCP Theorem with poly-logarithmic number of queries
2. Background on Coding Theory (two lectures)
3. Zero testing and Sum-check (a proof of a weak PCP Theorem modulo low degree testing)
5. Low degree testing (two lectures)
6. Wrapping up: PCP Theorem with poly-logarithmic number of queries (two lectures)
PCP Theorem with
constant number of queries
7. Background on expanders (two lectures)
8. Composition and degree reduction (two lectures)
9. An alternative proof via gap amplification (two lectures)
PCP Theorem with
low error
10. Background on information theory
11. The parallel repetition theorem (two lectures)
Optimal hardness of
approximation results
12. Background on Fourier analysis (two lectures)
13. Dictator testing, The Unique Games Conjecture (three lectures)