What is the nature of topological phenomena in condensed matter physics and quantum entanglement? Topological phenomena are the phenomena which are determined by some topological structure in the physical system, which are thus usually universal and robust against perturbations. For example, two famous topological phenomena are the flux quantization in superconductors and Hall conductance quantization in the Quantum Hall states. Recent discovery of topological insulators and topological superconductors in different symmetry classes bring the opportunity to study a large family of new topological phenomena. For example the three-dimensional topological insulator provides a condensed matter realization of the important theoretical concepts in high energy physics such as the ”theta-vacuum” and “axion”. The interplay of topological insulators and superconductors with conventional phases of matter such as ferromagnets and superconductors lead to richer topological phenomena.