Lecture 2: Hierarchy Theorems (Time, Space, and Nondeterministic) (15-855)

Lecture 3: Hopcroft--Paul--Valiant Theorem (15-855)

Lecture 4: Circuits (15-855)

Lecture 5: Probabilistic Complexity Classes (15-855)

Lecture 6: Quasilinear Cook--Levin Theorem (15-855)

Lecture 7: The Polynomial Time Hierarchy (15-855)

Lecture 8: Oracles, and the Polynomial Time Hierarchy vs. circuits (15-855)

Lecture 9: Time/Space Tradeoffs for SAT (15-855)

Lecture 10: Introduction to Arthur-Merlin classes, MA and AM (15-855)

Lecture 11: More on constant-round interactive proof systems (15-855)

Lecture 12: Approximate counting (15-855)

Lecture 13: Valiant--Vazirani Theorem, and Exact Counting (#P) (15-855)

Lecture 14: Toda's 1st Theorem and the Permanent (15-855)

Lecture 20: Permanent is #P-complete (15-855)

Lecture 15: Algebraic Circuit Complexity (15-855)

Lecture 16: Instance Checking and the Permanent (15-855)

Lecture 17: IP = PSPACE (15-855)