In this talk, we will study the manifolds with lower Ricci curvature  bound. First, we will introduce the Cheeger-Colding-Tian theory about the singular-regular analysis for Ricci limit space, and some progress by Colding-Naber, Cheeger-Naber. Later we will introduce some applications of this theory.  At last, we will talk about recent progress on the structure of the singular set based on joint work with Naber,  Cheeger and Naber. 

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