Ricci curvature occurs in the Einstein equation, Ricci flow, optimal transport, and is important both in mathematics and physics. Comparison method is one of the key tools in studying the Ricci curvature. We will start with Bochner formula and derive Laplacian comparison, Bishop-Gromov volume comparison, first eigenvalue and heat kernel comparison and some application. Then we will discuss some of its generalizations to Bakry-Emery Ricci curvature and integral Ricci curvature.