Circuit Complexity Theory

Khrapchenko's Theorem and its applications, Nechiporuk's Theorem, Random Restriction 

Subbotovskaya's lower bound on formula size, Andreev function, Polynomial sized monotone formula for majority (Valiant's Theorem) 

Complexity of basic arithmetic operations - addition, multiplication, division 

Bounded depth circuits, the complexity classes, NC, AC and TC. Division, powering and iterated products in NC (Beame-CookHoover Theorem) 

Uniform model of computation - Turing machines and its relationship with circuits 

Method of approximations, monotone lower bound on cliques of small size 

Monotone lower bound on cliques of arbitrary size 

Razborov-Smolensky lower bound for parity 

Lower bound for parity using Hastad's Switching Lemma 

Communication complexity and its relation to circuit complexity, Karchmer-Wigderson Theorem 

Recent advances in circuit lower bounds