Battery or battery cell module, comprising a number of battery cells, in particular lithium-ion battery cells, comprising in each case: a housing and, in the housing, at least one electrode assembly, in which electrodes are arranged in more than two layers in a cross section, the housing having at least two housing elements (11, 12) that separate the electrode assembly from the surroundings, wherein a first housing element is electrically connected to the positive pole of the electrode assembly, and wherein a second housing element is electrically connected to the negative pole of the electrode assembly, so that the battery cell can be electrically contacted on the first housing element and on the second housing element, wherein opposite end faces of the housing are formed either by the first or the second housing element (11, 12), wherein contacts (17, 18) between the first housing element and the positive pole of the electrode assembly and beween the second housing element and the negative pole of the electrode assembly are formed respectively on one of these opposite end faces of the battery cell, and opposite side faces of the housing are formed by the first and the second housing part (11, 12), wherein the first housing element and the second housing element are respectively designed in the form of a half-shell and are aligned with their open sides in relation to one another, the battery cell also comprising an insulating element, which is arranged between the housing elements (11, 12), and with which an electrical short-circuit between the first housing element and the second housing element can be prevented, characterized in that the first housing element of a first battery cell on a side face of the housing is connected in an electrically conductive manner to a second housing element of a second battery cell and the second housing element of the first battery cell on the same side face is connected in an electrically conductive manner to a first housing element of a third battery cell. a housing and, in the housing, at least one electrode assembly, in which electrodes are arranged in more than two layers in a cross section, the housing having at least two housing elements (11, 12) that separate the electrode assembly from the surroundings, wherein a first housing element is electrically connected to the positive pole of the electrode assembly, and wherein a second housing element is electrically connected to the negative pole of the electrode assembly, so that the battery cell can be electrically contacted on the first housing element and on the second housing element, wherein opposite end faces of the housing are formed either by the first or the second housing element (11, 12), wherein contacts (17, 18) between the first housing element and the positive pole of the electrode assembly and beween the second housing element and the negative pole of the electrode assembly are formed respectively on one of these opposite end faces of the battery cell, and opposite side faces of the housing are formed by the first and the second housing part (11, 12), wherein the first housing element and the second housing element are respectively designed in the form of a half-shell and are aligned with their open sides in relation to one another, the battery cell also comprising an insulating element, which is arranged between the housing elements (11, 12), and with which an electrical short-circuit between the first housing element and the second housing element can be prevented, characterized in that the first housing element of a first battery cell on a side face of the housing is connected in an electrically conductive manner to a second housing element of a second battery cell and the second housing element of the first battery cell on the same side face is connected in an electrically conductive manner to a first housing element of a third battery cell.