Starting with the general background of physics and condensed matter physics，the author describes he awarded achievements of 2016 Nobel Prize in Physics，as well as their scientific backgrounds and later development. After exposing the phase and phase transitions，the author explains how topological phase transitions go around the constraint of the dimension，how topology is the key to the essence of quantum Hall effect and leads to Chern insulator，as well as how topology makes the one-dimensional antiferromagnet depends on whether the spin quantum number is an integer or a half-integer.