Abstract: This is Shiing-Shen Chern's original work on Chern classes. In this talk, we will discuss three things: 1. Any complex vector bundle has a Hermitian structure. 2. Due to the Hermitian holomorphic structure, the formulas for the canonical connection and its curvature are very simple and easy to calculate. 3. More examples of Chern classes will be computed through Chern-Weil's theory.