NOVELTY - The energy storage device comprises an energy storage cell having an electrode stack (2) or an electrode winding. An outer functional layer (10) is provided on an outer wall of the electrode stack or electrode winding. The outer functional layer comprises a carrier layer that is partially permeable to substances. The carrier layer is coated with an inorganic material or an organic material on its one side, and is formed from a non-woven fabric. The inorganic material is ion-conductive in a temperature of -40 to 200 degrees C. The inorganic material has a particle size of 100 nm.    USE - The energy storage device is useful in a battery device for supplying an electric drive or a hybrid drive of a motor car with electrical power (all claimed).    ADVANTAGE - The energy storage device can be economically and easily manufactured with simple structure, enhanced functional reliability, improved mechanical and chemical stability, increased operational safety and long service life.    DETAILED DESCRIPTION - The energy storage device comprises an energy storage cell having an electrode stack (2) or an electrode winding. An outer functional layer (10) is provided on an outer wall of the electrode stack or electrode winding. The outer functional layer comprises a carrier layer that is partially permeable to substances. The carrier layer is coated with an inorganic material or an organic material on its one side, and is formed from a non-woven fabric. The inorganic material is ion-conductive in a temperature of -40 to 200 degrees C. The inorganic material has a particle size of 100 nm. The outer function layer is non-electron conductive or partially electron-conductive, has the shape of a half-shell, which surrounds a part of the energy storage cell, and is more shrinkable under thermal effect so that a part of the energy store cell is surrounded by the shrunk outer function layer. The energy storage device further comprises a container for receiving the energy store cell. The electrode stack and/or electrode winding are held together by the function layer. The container has an open-ended hollow body, which is cuboid shaped with two outwardly curved end faces. An INDEPENDENT CLAIM is included for a battery device.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of an energy storage device.    Electrode stack (2)    Insulating element (7)    Cover (8)    Opening (9)    Outer functional layer. (10)