A laboratory experiment on the reconnection of magnetic field lines in plasmas has been performed. A large-volume stationary plasma is produced and a time-varying magnetic field is applied to it. In vacuum the field exhibits an X-type neutral point on axis. Because of the time variation, plasma flows across the separatrix and currents along the separator are induced. The plasma currents modify the magnetic field topology. Flat neutral sheets are observed when flux is transferred across the separatrix into regions of common flux. Forced tearing and magnetic island formation occur in the return phase of the flux. An axial magnetic field is applied along the neutral line. This first part of the report mainly deals with the magnetic field topologies, but subsequent reports will present observations of plasma properties, anomalous resistivity, particle heating, and acceleration.