TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: The positive electrode contains positive electrode active material containing lithium-containing olivine-type phosphate comprising iron, cobalt, nickel or manganese, or lithium complex metal oxide in which the metal is chosen from nickel, manganese and cobalt. The negative electrode contains negative electrode active material containing lithium metal, lithium alloy, carbon material which occlude and release lithium, tin, tin compound, silicon, silicon compound or lithium titanate compound.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Composition: The phosphate (I) is chosen from methyl-2-(diethoxyphosphoryl)acetate, 2-propynyl-2-(dimethoxyphosphoryl)acetate, ethyl-2-(diethoxyphosphoryl)acetate, 2-propenyl-2-(diethoxyphosphoryl)acetate, 2-propynyl-2-(diethoxyphosphoryl)acetate, 2-propynyl-2-(dimethoxyphosphoryl)propanoate, 2-propynyl-2-(dimethoxy phosphoryl)propanoate, methyl-2-(diethoxyphosphoryl)-2-fluoroacetate, ethyl-2-(diethoxyphosphoryl)-2-fluoroacetate, 2-propenyl-2-(diethoxy phosphoryl)-2-fluoroacetate, 2-propynyl-2-(diethoxyphosphoryl)-2-fluoroacetate, methyl-2-(diethoxyphosphoryl)-2,2-difluoroacetate, ethyl-2-(diethoxyphosphoryl)-2,2-difluoroacetate, 2-propenyl-2-(diethoxyphosphoryl)-2,2-difluoroacetate and 2-propynyl-2-(diethoxyphosphoryl)-2,2-difluoroacetate. The cyclic sulfonate (II) is chosen from 1,2-oxathiolane-2,2-dioxide-4-yl acetate and 5,5-dimethyl-1,2-oxathiolane-4-one-2,2-dioxide. The cyclic anhydride is succinic acid anhydride. The succinic acid anhydride containing side chain having allylic hydrogen is chosen from 2-allyl succinic anhydride, 2-(1-pentene-3-yl)succinic acid anhydride, 2-(1-hexene-3-yl)succinic acid anhydride, 2-(1-heptene-3-yl)succinic acid anhydride, 2-(1-octene-3-yl)succinic acid anhydride, 2-(1-nonene-3-yl)succinic acid anhydride, 2-(3-butene-2-yl)succinic acid anhydride, 2-(2-methyl-allyl)succinic acid anhydride and 2-(3-methyl-3-butene-2-yl)succinic acid anhydride. The nonaqueous solvent contains cyclic carbonate chosen from ethylene carbonate, propylene carbonate, 1,2-butylene carbonate, 2,3-butylene carbonate, 4-fluoro-1,3-dioxolane-2-one, trans or cis-4,5-difluoro-1,3-dioxolane-2-one, vinylene carbonate, vinyl ethylene carbonate, and 4-ethynyl-1,3-dioxolane-2-one, and chain-shaped ester or chain carboxylic acid ester. The chain-shaped ester is asymmetrical linear carbonate chosen from methyl ethyl carbonate, methyl propyl carbonate, methyl isopropyl carbonate, methyl butyl carbonate and ethyl propyl carbonate, or symmetrical linear carbonate chosen from dimethyl carbonate, diethyl carbonate, dipropyl carbonate, and dibutyl carbonate. The electrolyte salt is chosen from 11 lithium salts e.g. lithium hexafluorophosphate, lithium tetrafluoroborate, bis(oxalate-O,O')lithium borate, difluoro bis(oxalate-O,O')lithium phosphate and tetrafluoro(oxalate-O,O')lithium phosphate. The concentration of lithium salt is 0.3-2.5 M with respect to nonaqueous solvent.