Nikolai Saveliev
\newcommand{\p}{\partial} \newcommand{\sign}{\operatorname{sign}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\ep}{\varepsilon} \newcommand{\Th}{{\bold\Theta}^3_{\Bbb Z}} \newcommand{\bz}{{\Bbb Z}} \renewcommand{\fbox}{} \newcommand{\lattice}{} In this paper we present our results on the homology cobordism group $\Th$ of the oriented integral homology 3-spheres. We specially emphasize the role played in the subject by the gauge theory including Floer homology and invariants by Donaldson and Seiberg -- Witten.