Battery having at least two battery modules (1, 101, 102), wherein a battery module (1, 101, 102) comprises, respectively, a plurality of battery cells, in particular lithium-ion battery cells that are interconnected electrically in series and/or in parallel, and in addition has a positive voltage tap and a negative voltage tap, wherein a first module connecting element is connected in an electrically conductive manner to the positive voltage tap, and/or a second module connecting element is connected in an electrically conductive manner to the negative voltage tap, wherein a module connecting element (7, 8) of a first battery module and a module connecting element (7, 8) of a second battery module are connected in an electrically conductive manner, wherein the electrically conductive connection of the module connecting elements (7, 8) is realized as a plug-in connection, wherein a battery module (1, 101, 102) in each case has substantially two mutually opposite end faces, two mutually opposite side faces, and one battery-module underside that is opposite one battery-module upper side, wherein the positive voltage tap and/or the negative voltage tap of the battery module (1, 101, 102) are/is arranged on the battery-module upper side, wherein the first battery module and the second battery module are arranged next to each other, and one of the two end faces of the first battery module is arranged directly adjacently to one of the two end faces of the second battery module, and the first module connecting element and/or the second module connecting element are/is arranged on a side face, or in that the first battery module and the second battery module are arranged next to each other, and one of the two side faces of the first battery module is arranged directly adjacently to one of the two side faces of the second battery module, and the first module connecting element and/or the second module connecting element are/is arranged on an end face, wherein a module connecting element (7, 8) in each case comprises a housing, composed of an electrically insulating material, arranged in which is an electrically conductive connecting portion (10, 11, 12) that is additionally connected in an electrically conductive manner to the positive voltage tap or to the negative voltage tap of the respective battery module (1, 101, 102), wherein, for the purpose of connecting the first battery module and the second battery module in an electrically conductive manner, a first connecting portion of the module connecting element of the first battery module and a second connecting portion of the module connecting element of the second battery module are connected to each other in an electrically conductive manner, characterized in that, for the purpose of direct electrically conductive connection, the first connecting portion has an opening, in which the second connecting portion, realized as a plug-in element, is arranged, or in that the first connecting portion has an opening, and the second connecting portion has an opening that extends continuously through the housing of the module connecting element having the second connecting portion, wherein a further electrically conductive connecting element is arranged such that it extends in the opening of the first connecting portion and in the opening of the second connecting portion.