NOVELTY - A battery has positive electrode (21) including positive electrode current collector having pair of surfaces, and positive electrode active material layer, negative electrode (22), separator (23) and electrolyte. The positive electrode active material layer contains positive electrode active material having compound(s) chosen from lithium nickel composite oxide having nickel as main component, lithium nickel cobalt manganese composite oxide having layer structure, lithium manganese composite oxide having spinel structure, and lithium iron phosphate compound having an olivine structure.    USE - Battery is used for battery pack, electronic apparatus, electric vehicle, electrical storage apparatus and electricity system (all claimed). Uses include but are not limited to laptop, cellular phone, cordless telephone handset, digital still camera, electronic book, music player, radio, headphone, game machine, memory cards, golf cart, electric cart, etc.    ADVANTAGE - The battery has high charging/discharging characteristics.    DETAILED DESCRIPTION - A battery has positive electrode including positive electrode current collector having pair of surfaces, and positive electrode active material layer provided on each of surfaces of positive electrode current collector, a negative electrode, a separator and electrolyte. The positive electrode active material layer contains positive electrode active material having compound(s) chosen from lithium nickel composite oxide having nickel as main component, lithium nickel cobalt manganese composite oxide having a layer structure, lithium manganese composite oxide having spinel structure, and a lithium iron phosphate compound having an olivine structure. The lithium iron phosphate compound contains at least lithium, iron and phosphorus. The positive electrode active material layer has area density (S) of 30 mg/cm2 or more. The lithium nickel composite oxide has a layer structure, and contains lithium and nickel with high content of nickel. The lithium nickel cobalt manganese composite oxide contains lithium, nickel, cobalt and manganese with low content of nickel. The lithium manganese composite oxide contains at least lithium and manganese. The separator includes a porous film having porosity ( epsilon (%)) and air permeability (t (sec/100 cc)) which satisfy relations: t=ax Ln( epsilon )-4.02a+100, where a is -1.87x 1010x S-4.96 to -40, and Ln is natural logarithm. INDEPENDENT CLAIMS are included for the following:    (1) battery pack;    (2) electronic apparatus;    (3) electric vehicle;    (4) electrical storage apparatus; and    (5) electricity system.    DESCRIPTION OF DRAWING(S) - The drawing shows a cross-sectional view of the secondary battery.    Battery lid (13)    Gasket (18)    Positive electrode (21)    Negative electrode (22)    Separator (23)