Abstract: In this talk, we will consider the Gromov-Hausdorff limit space (X,d) of a sequence of n-manifolds 

with lower Ricci curvature bound and noncollapsed volume. The limit space has a singular-regular

decomposition X=R\cup S and dim S<=n-2 proved by Cheeger-Colding. In this talk we will study the structure

of the singular set S and show that the singular set is (n-2)-rectifiable. We will also discuss the quantitative

estimate of the singular set. The proofs are based on some new estimates on neck regions and a

decomposition the orem which covers a general ball by neck regions and good balls. Our main focus in this talk

is the proof of the decomposition theorem.  This is a joint work with Jeff Cheeger and Aaron Naber.