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In the harsh environment of the Large Hadron Collider at CERN (design luminosity of 1034 cm-2s-1) efficient reconstruction of vertices is crucial for many physics analyses. Described in this paper is the expected performance of the vertex reconstruction used in the ATLAS experiment. The algorithms for the reconstruction of primary and secondary vertices as well as for finding photon conversions and vertex reconstruction in jets are described. The implementation of vertex algorithms which follows a very modular design based on object-oriented C++ is presented. A user-friendly concept allows event reconstruction and physics analyses to compare and optimize their choice among different vertex reconstruction strategies. The performance of implemented algorithms has been studied on a variety of Monte Carlo samples and results are presented.