Structure of non-smooth spaces with Ricci curvature bounded below

This thesis is devoted to the study of structural properties of non-smooth spaces with Ricci curvature bounded from below. The first part concerns with the structure theory of RCD(K,N) spaces: we prove the existence of the so-called essential dimension, along with rectifiability properties of the regular set. This theory is a result of many contributions [43,72,91,95,109,121], in our presentation we closely follow the recent works [41,43]. The second part of this thesis deals with codimension-1 structures on RCD(K,N) spaces. More precisely we study structural properties of boundaries of sets with finite perimeter, generalising the celebrated De Giorgi theory [65, 66] to this framework. This is based on the works [7,40].