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)