A lighting system comprising: a set of interconnected reconfigurable illuminating modules and corresponding removably attachable intermediate connectors , wherein (i) each illuminating module includes a light source and at least one connecting area , each connecting area including an illuminating module coupling assembly having at least one ferromagnetic member and having a set of electrically conductive members electrically coupled to the light source; (ii) each intermediate connector has a plurality of intermediate connector coupling assemblies electrically coupled to one another, each intermediate connector coupling assembly including a ferromagnetic component configured to be magnetically coupled to the at least one ferromagnetic member so that one intermediate connector coupling assembly is electrically coupled to one illuminating module coupling assembly, the two coupling assemblies being held in electrical contact with one another by magnetic force; and wherein the at least one ferromagnetic member is one of the electrically conductive members electrically coupled to the light source; characterized in that each of the plurality of intermediate connector coupling assemblies, of a selected one of the intermediate connectors , is adjustably mounted in the selected intermediate connector, so that an insertion axis of such coupling assembly can be oriented in a desired relationship to insertion axes of the other intermediate connector coupling assemblies of the selected one of the intermediate connectors. a set of interconnected reconfigurable illuminating modules and corresponding removably attachable intermediate connectors , wherein (i) each illuminating module includes a light source and at least one connecting area , each connecting area including an illuminating module coupling assembly having at least one ferromagnetic member and having a set of electrically conductive members electrically coupled to the light source; (ii) each intermediate connector has a plurality of intermediate connector coupling assemblies electrically coupled to one another, each intermediate connector coupling assembly including a ferromagnetic component configured to be magnetically coupled to the at least one ferromagnetic member so that one intermediate connector coupling assembly is electrically coupled to one illuminating module coupling assembly, the two coupling assemblies being held in electrical contact with one another by magnetic force; and (i) each illuminating module includes a light source and at least one connecting area , each connecting area including an illuminating module coupling assembly having at least one ferromagnetic member and having a set of electrically conductive members electrically coupled to the light source; (ii) each intermediate connector has a plurality of intermediate connector coupling assemblies electrically coupled to one another, each intermediate connector coupling assembly including a ferromagnetic component configured to be magnetically coupled to the at least one ferromagnetic member so that one intermediate connector coupling assembly is electrically coupled to one illuminating module coupling assembly, the two coupling assemblies being held in electrical contact with one another by magnetic force; and wherein the at least one ferromagnetic member is one of the electrically conductive members electrically coupled to the light source; characterized in that each of the plurality of intermediate connector coupling assemblies, of a selected one of the intermediate connectors , is adjustably mounted in the selected intermediate connector, so that an insertion axis of such coupling assembly can be oriented in a desired relationship to insertion axes of the other intermediate connector coupling assemblies of the selected one of the intermediate connectors. <EOS>