New Developments in the Search for the Topology of the Universe

Multi-connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search of the topology of the universe focusing on three dimensional methods. We present the crystallographic method, we give a new lower bound on the size of locally Euclidean multi-connected universe model of $3000 h^{-1} \hbox{Mpc}$ based on this method and a quasar catalog, we discuss its successes and failures, and the attemps to generalise it. We finally introduce a new statistical method based on a collecting correlated pair (CCP) technique.