In the study of quantum phases, the concept of topological invariant has emerged as a new paradigm beyond that of Landau theory. The relevance of topology for the classification of phases has been known since the discovery of the quantum hall effect. However, recent theoretical and experimental discoveries of new topological insulators has led to a renewed interest. The purpose of this reading group is to explore both recent and classical results for topological insulators including but not limited to (1) bulk-boundary correspondence (2) K-theoretic classification of topological insulators (3) topological invariants in the presence of disorder (4) quantization of Hall conductance in interacting systems.