Spontaneous Symmetry Breaking and Chiral Symmetry

In this introductory lecture, some basic features of the spontaneous symmetry breaking are discussed. More specifically, $\sigma$-model, non-linear realization, and some examples of spontaneous symmetry breaking in the non-relativistic system are discussed in details. The approach here is more pedagogical than rigorous and the purpose is to get some simple explanation of some useful topics in this rather wide area. .