Electrical energy storage module, having: at least one storage cell stack, which has: a multiplicity of energy storage cells (10; 20), which each have electrode elements and a cell housing, wherein the electrode elements are electrically connected to in each case one of two cell pole connections (1a; 1b) formed at opposite side faces of the cell housing, and wherein the multiplicity of energy storage cells (10; 20) are arranged in series in the storage cell stack in such a way that in each case two cell pole connections (1a; 1b) of adjacent energy storage cells (10; 20) of different polarity in direct physical contact are electrically connected to one another in planar fashion, furthermore having: a planar contact element, which makes electrical contact with an energy storage cell, which is arranged at a first end face of the storage cell stack, at the cell pole connection facing the first end face; and a first planar pole contact connection, which makes electrical contact with an energy storage cell, which is arranged at a second end face of the storage cell stack, which second end face is located opposite the first end face, at the cell pole connection facing the second end face, characterized by a planar contact connector, which is arranged at a side face of the storage cell stack and which makes electrical contact with the planar contact element. a multiplicity of energy storage cells (10; 20), which each have electrode elements and a cell housing, wherein the electrode elements are electrically connected to in each case one of two cell pole connections (1a; 1b) formed at opposite side faces of the cell housing, and wherein the multiplicity of energy storage cells (10; 20) are arranged in series in the storage cell stack in such a way that in each case two cell pole connections (1a; 1b) of adjacent energy storage cells (10; 20) of different polarity in direct physical contact are electrically connected to one another in planar fashion, furthermore having: a planar contact element, which makes electrical contact with an energy storage cell, which is arranged at a first end face of the storage cell stack, at the cell pole connection facing the first end face; and a first planar pole contact connection, which makes electrical contact with an energy storage cell, which is arranged at a second end face of the storage cell stack, which second end face is located opposite the first end face, at the cell pole connection facing the second end face, characterized by a planar contact connector, which is arranged at a side face of the storage cell stack and which makes electrical contact with the planar contact element. a planar contact element, which makes electrical contact with an energy storage cell, which is arranged at a first end face of the storage cell stack, at the cell pole connection facing the first end face; and a first planar pole contact connection, which makes electrical contact with an energy storage cell, which is arranged at a second end face of the storage cell stack, which second end face is located opposite the first end face, at the cell pole connection facing the second end face, characterized by a planar contact connector, which is arranged at a side face of the storage cell stack and which makes electrical contact with the planar contact element.