The discovery of laser cooling and magneto-optical trapping was awarded with the 1997 Noble Price in physics. Since then quantum atom optics has become one of the most active research areas in experimental physics. In this thesis Oliver Gugenberger gives a vivid description of the operation principle of magneto-optical trapping and how it is possible to perform single atom experiments based on this method. He designed a special-magneto optical trap at the Vienna University of Technology which will be used in upcoming experiments to trap and entangle single Rubidium atoms as a possible...