Abstract: In this talk, first I mainly introduce some important results of the shrinking gradient Ricci solitons. Secondly, I will introduce some results of the shrinking gradient Ricci solitons: (1) Volume growth; (2) A gap theorem; (3)Classification of Kahler case for nonnegative holomorphic bisectional (or orthogonal bisectional ) curvature. The bisectional curvature part of (3) is a joint work with Guoqiang Wu.